# Tagged Questions

Questions about the evaluation of specific definite integrals.

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### Derivativation of definite integral

Having: $f = \int_0^{n}{X_{(t)}dt} + X_{n}$ How can I find: $\frac{\partial{f}}{\partial{n}} = ?$ Please note that the derivative is done with respect to one of the ends of the integral. (hope ...
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### Is it possible to evaluate this integral? [duplicate]

Is it possible to evaluate this integral: $$\int_{0}^{\frac{\pi }{2}}\ln(\sin 2x){\rm d}x$$
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### Tricky elementary integral

$$\int_{0}^{\frac{\pi }{2}}x\cot(x)dx$$ I tried integration by parts and got $\frac{1}{2}\int_{0}^{\frac{\pi }{2}}x^{2} \csc^{2}x dx$ which doesn't help at all. I don't really know what to do. Any ...
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### A “tricky” integral: $\int_0^{\infty} t e^{-nct} (1-e^{-ct})^m dt$

In an article in the current (May 2013) issue of the College Mathematics Journal, they say that the following integral is "tricky to evaluate": $\int_0^{\infty} t e^{-nct} (1-e^{-ct})^m dt$ where ...
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### Not getting $-\frac{\pi}{4}$ for my integral. Help with algebra

Evaluate $$\int_0^\infty \dfrac {\log{x}}{(x^2+1)^2}dx$$ I've been working on this problem for half the day. I'm not getting anywhere. 1) I first changed the integral from negative infinity to ...
### How to calculate the limit $\lim_{n\rightarrow\infty} n\int^{1}_{0}x^{kn}e^{x^{n}}dx$
Let $k$ be a fixed positive integer. How to calculate the following limit? $$\lim_{n\rightarrow\infty} n\int^{1}_{0}x^{kn}e^{x^{n}}dx$$