List questions from integration-by-parts

Published on 23 Mar 2026 - 10:06

2.8k

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Reduction formula for $\int_0^{\pi/2}\cos^m\theta\sin^n\theta\,d\theta$

Published on 17 Nov 2015 - 19:43

224

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Most elegant method to calculate $\int^\pi_0 (x\sin x)^2 dx$

Published on 17 Nov 2015 - 20:54

183

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Compute $\int^1_0 \int^{x^2}_0\frac{y}{e^x} \, dy \, dx$

Published on 18 Nov 2015 - 0:36

84

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Why is $\int e^{-t}u(t) dt = (1-e^{-t})u(t) + Constant$?

Published on 18 Nov 2015 - 15:21

51

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I would like a hint for solving this indefinite integral

Published on 19 Nov 2015 - 5:23

114

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Integration (by parts?)

Published on 24 Mar 2026 - 22:30

737

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Trick for a definite integral

Published on 19 Nov 2015 - 23:41

144

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problem with integeration by parts

Published on 23 Nov 2015 - 9:40

90

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Definite Integral involving reciprocals of logs

Published on 02 Dec 2015 - 1:49

71

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Use integration by parts to evaluate each function

Published on 05 Dec 2015 - 10:05

86

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Basic integration by parts yields (seemingly?) wrong result

Published on 09 Dec 2015 - 20:30

62

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Use integration by parts to prove the equality.

Published on 28 Dec 2015 - 9:09

114

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Evaluate $\int_{0}^{1}{x\ln x dx}$.

Published on 29 Dec 2015 - 12:47

405

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How to compute $\int_0^{\frac{\pi}{2}} \frac{\ln(\sin(x))}{\cot(x)}\ \text{d}x$

Published on 05 Jan 2016 - 20:48

List Question

Repeated integration by parts of a definite integral

Reduction formula for $\int_0^{\pi/2}\cos^m\theta\sin^n\theta\,d\theta$

Most elegant method to calculate $\int^\pi_0 (x\sin x)^2 dx$

Compute $\int^1_0 \int^{x^2}_0\frac{y}{e^x} \, dy \, dx$

Why is $\int e^{-t}u(t) dt = (1-e^{-t})u(t) + Constant$?

I would like a hint for solving this indefinite integral

Integration (by parts?)

Trick for a definite integral

problem with integeration by parts

Definite Integral involving reciprocals of logs

Use integration by parts to evaluate each function

Basic integration by parts yields (seemingly?) wrong result

Use integration by parts to prove the equality.

Evaluate $\int_{0}^{1}{x\ln x dx}$.

How to compute $\int_0^{\frac{\pi}{2}} \frac{\ln(\sin(x))}{\cot(x)}\ \text{d}x$

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