Questions tagged [indefinite-integrals]

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

3,694 questions
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$\int\frac{dx}{x(x+1)(x+2)\cdot\space…\space\cdot(x+n)}$ [duplicate]

I've been trying to solve explicitly the following indefinite integral: $$\int\frac{dx}{x(x+1)(x+2)\cdot\space...\space\cdot(x+n)}$$ I tried to perform partial fraction decomposition, and after ...
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Integrating this beast $\int\frac{3}{x\sqrt{x^2+9}}dx$ [closed]

How do I integrate this beast $$\int\frac{3}{x\sqrt{x^2+9}}dx?$$ Using the substitution $t = \frac{1}{x}$ (the substitution is given). My attempt: https://imgur.com/YSVXMdI alternative sub: t = a ...
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1st order differential linear equation, question on absolute value

I'm trying to find the general solution to this equation: $$x \frac{dy}{dx}+3(y+x^2)=\frac{\sin(x)}{x}$$ Standard form puts it like this: $$\frac{dy}{dx}+\frac{3}{x}y=\frac{\sin(x)-3x^3}{x^2}$$ To ...
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How to find asymptotics of indefinite integrals

Often, an indefinite integral cannot be expressed exactly. It would be useful if it were possible to at least prove something about asymptotics of the indefinite integral. I wasn't able to find much ...
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How to reduce an integral with square root of cubic function into an elliptic integral

I need to calculate the following ntegral: $$\int \frac{t }{\sqrt{2 t^3 - 3 t^2 + 6 C}} dt$$ where $C$ is a constant to be determined later, so I cannot look for roots of the polynomial in the ...
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How to find $\int \sum_{n=0}^\infty \frac {(\ln x)^n}{x^n.n!}dx$?

I know how to find the integral of a normal power series like the power series of $\sin (x)$, but have no idea how to integrate the $( \ln x )^n$ term inside the summation.
What is the series expansion of $\sqrt[x] x$?
What is the series expansion of $\sqrt[x] x$ ? I want to find it because I want to find $\int \sqrt[x] x dx$ but believe that the integral cannot be expressed in the form of elementary functions.