Integration of two exponential multiplied by each otherIntegrating $sin^2(x)$ using imaginary numbers.Need...
How do I prevent a homebrew Grappling Hook feature from trivializing Tomb of Annihilation?
Does an Eldritch Knight's Weapon Bond protect him from losing his weapon to a Telekinesis spell?
Does diversity provide anything that meritocracy does not?
When Are Enum Values Defined?
Equivalent of "illegal" for violating civil law
Which RAF squadrons and aircraft types took part in the bombing of Berlin on the 25th of August 1940?
Plausible reason for gold-digging ant
Is `Object` a function in javascript?
Why does 0.-5 evaluate to -5?
Does the US government have any planning in place to ensure there's no shortages of food, fuel, steel and other commodities?
How to not let the Identify spell spoil everything?
Microtypography protrusion with Polish quotation marks
Website seeing my Facebook data?
Why did Luke use his left hand to shoot?
What can I do to encourage my players to use their consumables?
Possible issue with my W4 and tax return
Renting a 2CV in France
Critique vs nitpicking
What's the oldest plausible frozen specimen for a Jurassic Park style story-line?
The No-Straight Maze
Should I cite R or RStudio?
Am I correct in stating that the study of topology is purely theoretical?
Are the positive and negative planes inner or outer planes in the Great Wheel cosmology model?
Why do neural networks need so many training examples to perform?
Integration of two exponential multiplied by each other
Integrating $sin^2(x)$ using imaginary numbers.Need help with integration by partsIntegrate $int frac{ln(sin x)}{sin^2 x},mathrm dx.$Integral $int frac{sqrt{16-x^2}}{x} mathrm{d}x$Solid Angle IntegrationDouble Integral of an Exponential Function with an Absolute Value in the Numerator of the ExponentComplex integral with exponential and tangentShow the value of an integral using integration by parts.How to calculate $int xe^{1/x^2} dx$How to integrate $int 2xe^{x^2-y^2}cos(2xy)- 2ye^{x^2-y^2}sin(2xy) mathrm dy$?
$begingroup$
I am having confusion on how to go about integrating this integral:
$$int[exp( jcdotphicdot x)cdot exp(jcdot kcdot xcdot sin theta)] mathrm dx.$$
I attempted by using integration by parts but that didn't work.
integration
edited 2 hours ago
Thomas Shelby
3,6342525
asked 3 hours ago
articatarticat
163
$endgroup$
add a comment |
$begingroup$
I am having confusion on how to go about integrating this integral:
$$int[exp( jcdotphicdot x)cdot exp(jcdot kcdot xcdot sin theta)] mathrm dx.$$
I attempted by using integration by parts but that didn't work.
integration
edited 2 hours ago
Thomas Shelby
3,6342525
asked 3 hours ago
articatarticat
163
$endgroup$
$begingroup$
This is a bit off-topic, but you might have encountered problems, with integrands like exp(x) * sin(x) where you needed to do two rounds of integration by parts. Using complex exponentials lets you avoid integration by parts in those problems by putting everything in one exponential.
$endgroup$
– Gus
1 hour ago
add a comment |
$begingroup$
I am having confusion on how to go about integrating this integral:
$$int[exp( jcdotphicdot x)cdot exp(jcdot kcdot xcdot sin theta)] mathrm dx.$$
I attempted by using integration by parts but that didn't work.
integration
edited 2 hours ago
Thomas Shelby
3,6342525
asked 3 hours ago
articatarticat
163
$endgroup$
I am having confusion on how to go about integrating this integral:
$$int[exp( jcdotphicdot x)cdot exp(jcdot kcdot xcdot sin theta)] mathrm dx.$$
I attempted by using integration by parts but that didn't work.
integration
integration
edited 2 hours ago
Thomas Shelby
3,6342525
asked 3 hours ago
articatarticat
163
edited 2 hours ago
Thomas Shelby
3,6342525
asked 3 hours ago
articatarticat
163
edited 2 hours ago
Thomas Shelby
3,6342525
edited 2 hours ago
Thomas Shelby
3,6342525
edited 2 hours ago
Thomas Shelby
3,6342525
3,6342525
asked 3 hours ago
articatarticat
163
asked 3 hours ago
articatarticat
163
asked 3 hours ago
articatarticat
163
163
$begingroup$
This is a bit off-topic, but you might have encountered problems, with integrands like exp(x) * sin(x) where you needed to do two rounds of integration by parts. Using complex exponentials lets you avoid integration by parts in those problems by putting everything in one exponential.
$endgroup$
– Gus
1 hour ago
add a comment |
$begingroup$
This is a bit off-topic, but you might have encountered problems, with integrands like exp(x) * sin(x) where you needed to do two rounds of integration by parts. Using complex exponentials lets you avoid integration by parts in those problems by putting everything in one exponential.
$endgroup$
– Gus
1 hour ago
$begingroup$
This is a bit off-topic, but you might have encountered problems, with integrands like exp(x) * sin(x) where you needed to do two rounds of integration by parts. Using complex exponentials lets you avoid integration by parts in those problems by putting everything in one exponential.
$endgroup$
– Gus
1 hour ago
$begingroup$
This is a bit off-topic, but you might have encountered problems, with integrands like exp(x) * sin(x) where you needed to do two rounds of integration by parts. Using complex exponentials lets you avoid integration by parts in those problems by putting everything in one exponential.
$endgroup$
– Gus
1 hour ago
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Recall that $e^acdot e^b=e^{a+b} $. So we can write $$intexp( jcdotphicdot x)cdot exp(jcdot kcdot xcdotsin theta) mathrm dx=intexpleft(( jcdot phi+jcdot kcdotsin theta)xright) mathrm dx=dfrac1 { jcdotphi+jcdot kcdotsin theta}expleft(( jcdot phi+jcdot kcdotsin theta)xright).$$
answered 3 hours ago
Thomas ShelbyThomas Shelby
3,6342525
$endgroup$
add a comment |
$begingroup$
Hint: exponentiation rules. $$exp(acdot x)cdotexp(bcdot x)=exp((a+b)cdot x)$$
answered 3 hours ago
Graham KempGraham Kemp
86.1k43478
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3126893%2fintegration-of-two-exponential-multiplied-by-each-other%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Recall that $e^acdot e^b=e^{a+b} $. So we can write $$intexp( jcdotphicdot x)cdot exp(jcdot kcdot xcdotsin theta) mathrm dx=intexpleft(( jcdot phi+jcdot kcdotsin theta)xright) mathrm dx=dfrac1 { jcdotphi+jcdot kcdotsin theta}expleft(( jcdot phi+jcdot kcdotsin theta)xright).$$
answered 3 hours ago
Thomas ShelbyThomas Shelby
3,6342525
$endgroup$
add a comment |
$begingroup$
Recall that $e^acdot e^b=e^{a+b} $. So we can write $$intexp( jcdotphicdot x)cdot exp(jcdot kcdot xcdotsin theta) mathrm dx=intexpleft(( jcdot phi+jcdot kcdotsin theta)xright) mathrm dx=dfrac1 { jcdotphi+jcdot kcdotsin theta}expleft(( jcdot phi+jcdot kcdotsin theta)xright).$$
answered 3 hours ago
Thomas ShelbyThomas Shelby
3,6342525
$endgroup$
add a comment |
$begingroup$
Recall that $e^acdot e^b=e^{a+b} $. So we can write $$intexp( jcdotphicdot x)cdot exp(jcdot kcdot xcdotsin theta) mathrm dx=intexpleft(( jcdot phi+jcdot kcdotsin theta)xright) mathrm dx=dfrac1 { jcdotphi+jcdot kcdotsin theta}expleft(( jcdot phi+jcdot kcdotsin theta)xright).$$
answered 3 hours ago
Thomas ShelbyThomas Shelby
3,6342525
$endgroup$
Recall that $e^acdot e^b=e^{a+b} $. So we can write $$intexp( jcdotphicdot x)cdot exp(jcdot kcdot xcdotsin theta) mathrm dx=intexpleft(( jcdot phi+jcdot kcdotsin theta)xright) mathrm dx=dfrac1 { jcdotphi+jcdot kcdotsin theta}expleft(( jcdot phi+jcdot kcdotsin theta)xright).$$
answered 3 hours ago
Thomas ShelbyThomas Shelby
3,6342525
edited 3 hours ago
answered 3 hours ago
Thomas ShelbyThomas Shelby
3,6342525
answered 3 hours ago
Thomas ShelbyThomas Shelby
3,6342525
answered 3 hours ago
Thomas ShelbyThomas Shelby
3,6342525
3,6342525
add a comment |
add a comment |
$begingroup$
Hint: exponentiation rules. $$exp(acdot x)cdotexp(bcdot x)=exp((a+b)cdot x)$$
answered 3 hours ago
Graham KempGraham Kemp
86.1k43478
$endgroup$
add a comment |
$begingroup$
Hint: exponentiation rules. $$exp(acdot x)cdotexp(bcdot x)=exp((a+b)cdot x)$$
answered 3 hours ago
Graham KempGraham Kemp
86.1k43478
$endgroup$
add a comment |
$begingroup$
Hint: exponentiation rules. $$exp(acdot x)cdotexp(bcdot x)=exp((a+b)cdot x)$$
answered 3 hours ago
Graham KempGraham Kemp
86.1k43478
$endgroup$
Hint: exponentiation rules. $$exp(acdot x)cdotexp(bcdot x)=exp((a+b)cdot x)$$
answered 3 hours ago
Graham KempGraham Kemp
86.1k43478
answered 3 hours ago
Graham KempGraham Kemp
86.1k43478
answered 3 hours ago
Graham KempGraham Kemp
86.1k43478
answered 3 hours ago
Graham KempGraham Kemp
86.1k43478
86.1k43478
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3126893%2fintegration-of-two-exponential-multiplied-by-each-other%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
This is a bit off-topic, but you might have encountered problems, with integrands like exp(x) * sin(x) where you needed to do two rounds of integration by parts. Using complex exponentials lets you avoid integration by parts in those problems by putting everything in one exponential.
$endgroup$
– Gus
1 hour ago