How to evaluate this integral with exponent of an exponent?
I have the following integral which I need to evaluate but don't even know where to begin other than knowing I need to use u-substitution:
$$int_1^sqrt{3}2x^{x^{2}}$$
So far I know that $u=x^{2}$ and $du=2x$ but how do I evaluate this?
calculus integration indefinite-integrals
asked Nov 18 at 16:11
blizz
1345
add a comment |
I have the following integral which I need to evaluate but don't even know where to begin other than knowing I need to use u-substitution:
$$int_1^sqrt{3}2x^{x^{2}}$$
So far I know that $u=x^{2}$ and $du=2x$ but how do I evaluate this?
calculus integration indefinite-integrals
asked Nov 18 at 16:11
blizz
1345
1
You might consider writing $x^{x^2} = exp(log(x^{x^2}))$ and simplifying things a bit. Then try a substitution.
– Xander Henderson
Nov 18 at 16:17
maybe a parameterization so that you could differentiate under the integral sign?
– clathratus
Nov 18 at 21:38
@XanderHenderson what does it mean to write exp(log(x^x^2))? I might be a little slow now but not sure what that exp does...
– blizz
Nov 20 at 1:11
$exp(t) = mathrm{e}^t$.
– Xander Henderson
Nov 20 at 1:42
add a comment |
I have the following integral which I need to evaluate but don't even know where to begin other than knowing I need to use u-substitution:
$$int_1^sqrt{3}2x^{x^{2}}$$
So far I know that $u=x^{2}$ and $du=2x$ but how do I evaluate this?
calculus integration indefinite-integrals
asked Nov 18 at 16:11
blizz
1345
I have the following integral which I need to evaluate but don't even know where to begin other than knowing I need to use u-substitution:
$$int_1^sqrt{3}2x^{x^{2}}$$
So far I know that $u=x^{2}$ and $du=2x$ but how do I evaluate this?
calculus integration indefinite-integrals
calculus integration indefinite-integrals
asked Nov 18 at 16:11
blizz
1345
asked Nov 18 at 16:11
blizz
1345
asked Nov 18 at 16:11
blizz
1345
asked Nov 18 at 16:11
blizz
1345
asked Nov 18 at 16:11
blizz
1345
1345
1
You might consider writing $x^{x^2} = exp(log(x^{x^2}))$ and simplifying things a bit. Then try a substitution.
– Xander Henderson
Nov 18 at 16:17
maybe a parameterization so that you could differentiate under the integral sign?
– clathratus
Nov 18 at 21:38
@XanderHenderson what does it mean to write exp(log(x^x^2))? I might be a little slow now but not sure what that exp does...
– blizz
Nov 20 at 1:11
$exp(t) = mathrm{e}^t$.
– Xander Henderson
Nov 20 at 1:42
add a comment |
1
You might consider writing $x^{x^2} = exp(log(x^{x^2}))$ and simplifying things a bit. Then try a substitution.
– Xander Henderson
Nov 18 at 16:17
maybe a parameterization so that you could differentiate under the integral sign?
– clathratus
Nov 18 at 21:38
@XanderHenderson what does it mean to write exp(log(x^x^2))? I might be a little slow now but not sure what that exp does...
– blizz
Nov 20 at 1:11
$exp(t) = mathrm{e}^t$.
– Xander Henderson
Nov 20 at 1:42
1
1
You might consider writing $x^{x^2} = exp(log(x^{x^2}))$ and simplifying things a bit. Then try a substitution.
– Xander Henderson
Nov 18 at 16:17
You might consider writing $x^{x^2} = exp(log(x^{x^2}))$ and simplifying things a bit. Then try a substitution.
– Xander Henderson
Nov 18 at 16:17
maybe a parameterization so that you could differentiate under the integral sign?
– clathratus
Nov 18 at 21:38
maybe a parameterization so that you could differentiate under the integral sign?
– clathratus
Nov 18 at 21:38
@XanderHenderson what does it mean to write exp(log(x^x^2))? I might be a little slow now but not sure what that exp does...
– blizz
Nov 20 at 1:11
@XanderHenderson what does it mean to write exp(log(x^x^2))? I might be a little slow now but not sure what that exp does...
– blizz
Nov 20 at 1:11
$exp(t) = mathrm{e}^t$.
– Xander Henderson
Nov 20 at 1:42
$exp(t) = mathrm{e}^t$.
– Xander Henderson
Nov 20 at 1:42
add a comment |
active
oldest
votes
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%2f3003731%2fhow-to-evaluate-this-integral-with-exponent-of-an-exponent%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
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.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- 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.
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%2f3003731%2fhow-to-evaluate-this-integral-with-exponent-of-an-exponent%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
1
You might consider writing $x^{x^2} = exp(log(x^{x^2}))$ and simplifying things a bit. Then try a substitution.
– Xander Henderson
Nov 18 at 16:17
maybe a parameterization so that you could differentiate under the integral sign?
– clathratus
Nov 18 at 21:38
@XanderHenderson what does it mean to write exp(log(x^x^2))? I might be a little slow now but not sure what that exp does...
– blizz
Nov 20 at 1:11
$exp(t) = mathrm{e}^t$.
– Xander Henderson
Nov 20 at 1:42