List questions from improper-integrals

Published on 19 Oct 2014 - 21:34

450

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Evaluating $\int_0^1 \frac{t^{a-1}}{1-t}-\frac{ct^{b-1}}{1-t^c}\ dt$

Published on 20 Oct 2014 - 17:49

737

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Prove $\int_0^{2\pi}\frac{3a\sin^2\theta}{(1-a\cos \theta)^4}\mathrm{d}\theta = \int_0^{2\pi}\frac{\cos \theta}{(1-a\cos \theta)^3}\,\mathrm{d}\theta$

Published on 20 Oct 2014 - 20:01

380

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Evaluate integral: $\int_0^{+\infty}\frac{\cos{bx}-\cos{ax}}{x}dx$

Published on 21 Oct 2014 - 9:12

950

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Inverse Trigonometric Integrals

Published on 29 Mar 2026 - 13:47

1.5k

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Improper integral : $\int_0^{+\infty}\frac{x\sin x}{x^2+1}$

Published on 29 Mar 2026 - 13:46

794

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Find $\int_{ - \infty }^{ + \infty } {\frac{1} {1 + {x^4}}} \;{\mathrm{d}}x$

Published on 03 Apr 2026 - 19:03

71

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Improper integral: is it convergent?

Published on 22 Oct 2014 - 16:26

55

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Does there exist such function?

Published on 22 Oct 2014 - 16:53

55

Views

Definite integral substitution question.

Published on 22 Oct 2014 - 17:01

374

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How to evaluate $\int_0^1\frac{\tanh ^{-1}(x)\log(x)}{(1-x) x (x+1)} \operatorname d \!x$?

Published on 29 Mar 2026 - 13:40

40

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principal value integral with a singularity at t=1

Published on 23 Oct 2014 - 7:52

45

Views

Determine integral by using the following identity (which is imaginairy)?

Published on 23 Oct 2014 - 10:22

5.5k

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Integrating the gamma function

Published on 28 Mar 2026 - 20:03

237

Views

Test for convergence $\int_0^{\infty} \frac{\sin(x)}{x+\log(x)} \ dx$

Published on 24 Oct 2014 - 14:13

List Question

Is this integral in its most simplified form?

Evaluating $\int_0^1 \frac{t^{a-1}}{1-t}-\frac{ct^{b-1}}{1-t^c}\ dt$

Prove $\int_0^{2\pi}\frac{3a\sin^2\theta}{(1-a\cos \theta)^4}\mathrm{d}\theta = \int_0^{2\pi}\frac{\cos \theta}{(1-a\cos \theta)^3}\,\mathrm{d}\theta$

Evaluate integral: $\int_0^{+\infty}\frac{\cos{bx}-\cos{ax}}{x}dx$

Inverse Trigonometric Integrals

Improper integral : $\int_0^{+\infty}\frac{x\sin x}{x^2+1}$

Find $\int_{ - \infty }^{ + \infty } {\frac{1} {1 + {x^4}}} \;{\mathrm{d}}x$

Improper integral: is it convergent?

Does there exist such function?

Definite integral substitution question.

How to evaluate $\int_0^1\frac{\tanh ^{-1}(x)\log(x)}{(1-x) x (x+1)} \operatorname d \!x$?

principal value integral with a singularity at t=1

Determine integral by using the following identity (which is imaginairy)?

Integrating the gamma function

Test for convergence $\int_0^{\infty} \frac{\sin(x)}{x+\log(x)} \ dx$

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