List questions from improper-integrals

Published on 29 Mar 2026 - 15:41

323

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How to evaluate $\int_0^ \infty e^{-x\sinh(t)-\frac{1}{2}t}~dt$?

Published on 16 Apr 2014 - 2:21

2.1k

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Any general methods to calculate integral of $P(x)/Q(x)$ from $0$ to $\infty$?

Published on 28 Mar 2026 - 7:53

245

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How do I integrate this in terms of error function

Published on 16 Apr 2014 - 10:02

353

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What is the value of that integral?

Published on 18 Apr 2014 - 17:02

1.6k

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The Fourier transform of a power of the absolute value function (and a related integral)

Published on 18 Apr 2014 - 19:48

127

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Convergence of $\int_{0}^{+\infty}\ln(1+\frac{1}{t^2})$

Published on 18 Apr 2014 - 21:20

470

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Compute $I=\int_0^{+\infty}\frac{\arctan(t)}{e^{\pi t}-1}dt$

Published on 18 Apr 2014 - 21:50

279

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Why does $\int_1^\infty\frac{\sin^2(x)}{x}\mathrm d x$ diverge?

Published on 20 Apr 2014 - 12:47

4.8k

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Integral $\int_0^1 dx \frac{\ln x \ln^2(1-x)\ln(1+x)}{x}$

Published on 26 Mar 2026 - 12:53

214

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Taylor expansion of a not easily differentiable function

Published on 20 Apr 2014 - 18:46

95

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Integral question with square roots

Published on 21 Apr 2014 - 10:07

515

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Show that; $\displaystyle\int_0^\infty\frac{f(bx)-f(ax)}{x}dx=(l-f(0))\ln\frac{b}{a}$

Published on 21 Apr 2014 - 10:47

53

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Application of Residues

Published on 28 Mar 2026 - 10:17

191

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Show $\lim\limits_{a \rightarrow + \infty} \int_0^{\infty} \frac{1}{1+y^2}e^{-ay} dy =0 $

Published on 31 Mar 2026 - 16:23

List Question

Integral of $\sin|x|$

How to evaluate $\int_0^ \infty e^{-x\sinh(t)-\frac{1}{2}t}~dt$?

Any general methods to calculate integral of $P(x)/Q(x)$ from $0$ to $\infty$?

How do I integrate this in terms of error function

What is the value of that integral?

The Fourier transform of a power of the absolute value function (and a related integral)

Convergence of $\int_{0}^{+\infty}\ln(1+\frac{1}{t^2})$

Compute $I=\int_0^{+\infty}\frac{\arctan(t)}{e^{\pi t}-1}dt$

Why does $\int_1^\infty\frac{\sin^2(x)}{x}\mathrm d x$ diverge?

Integral $\int_0^1 dx \frac{\ln x \ln^2(1-x)\ln(1+x)}{x}$

Taylor expansion of a not easily differentiable function

Integral question with square roots

Show that; $\displaystyle\int_0^\infty\frac{f(bx)-f(ax)}{x}dx=(l-f(0))\ln\frac{b}{a}$

Application of Residues

Show $\lim\limits_{a \rightarrow + \infty} \int_0^{\infty} \frac{1}{1+y^2}e^{-ay} dy =0 $

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