Questions tagged [indefinite-integrals]

Question about finding the primitives of a given function, whether or not elementary.

3,695 questions
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Can someone help me to evaluate this triple integral that even Wolfram Alpha can't [on hold]

It's part of a classified project -- of a theory of everything in $n$-dimensions geometry. I spent 2 days trying to find calculators that shows the solution step-by-step, but I can't find anything... ...
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Why is this not a u-sub?

$\int e^*x dx$ Why is this not a u-sub? Where I let $u=x$ so $du=dx$ $\int e^udu = e^u +c$ I have notes where we did it as ab IBP problem instead.
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How to solve the indefinite integral?

The integral :- $$\int x^m \ln(a+x) \,dx.$$ (Also what is $m$ is not an integer, just an arbitrary real number?) I have found the integral in the book gradshteyn and ryzhik of which this is a ...
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Integral involving natural log exponential and sin: $\int\ln(e^x\sin^3x)\,dx$ [on hold]

How can I solve the following integral? $$\int\ln(e^x\sin^3x)\,dx$$
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Find $\int\sin^3(2x+1)dx$. [closed]

Find $\int\sin^3(2x+1)dx$. Having three different results which one is right right? 1.$y= -\frac{\cos (2x+1)}{2} +\frac{1}{24\cos(6x^3)} -\frac{1}{4\cos(2x+1)}+c$ $y=-\cos (2x+1) + \cos^3(2x+1) +c.$...
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Can u-substitution be used to solve integral where 'u' is NOT the inside function of a composite function?

I apologise in advance if this does not meet post guidelines. I am having difficulty with U-Substitution. I cannot seem to find an answer anywhere. Okay, so (if I'm not mistaken) u-substitution can ...
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Why this indefinite integral cannot be solved ?$\int\ln(x)\sqrt{x^{2 }+ ax + b}\, dx$ [closed]

I am trying to find a solution to this integral. However I have found nothing that helps, even wolfram alpha can not solve this integral. What would be the secret about it, since it looks so simple ? ...
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How to integrate $\sqrt{\arctan(x)}$ [closed]

How to do $$\int\sqrt{\arctan(x)}\, \mathrm dx \:???$$ Is there any other special function defined like this?
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Indefinite integration of $\int \frac{1}{1+\sqrt{x^2+2x+2}}dx$

Integrate $$\int \frac{1}{1+\sqrt{x^2+2x+2}}dx$$ I have tried by using Euler substitution, but that gave me a wrong answer. So can somebody help?
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Verifying an indefinite integral solution

I'm working on indefinite integrals right now. I'm given the problem $$\int(\frac{8}{x}-\frac{5}{x^2}+\frac{6}{x^3}) dx$$ My worksheet gives the answer $8\ln(x)+\frac{5}{x}-\frac{3}{x^2}+c$ I'm ...
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Integrate by parts - $\int\sqrt{a^2-x^2}dx$
Differentiate $\arcsin\left(\dfrac{x}{a}\right)$ with respect to x. Integrate by parts: $\int\sqrt{a^2-x^2}dx$ The answer to part one of the question is $\dfrac{1}{\sqrt{a^2-{x^2}}}$
As we know, the integral of $\frac{1}{x}$ is $ln(x)+c$. Because $x$ and $dx$ have the same dimension, $\int\frac{dx}{x}$ is dimensionless. But my problem is: $x$ is dimensional. I've been trained that ...