List questions from improper-integrals

Published on 12 Apr 2026 - 9:01

418

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$\int_{0}^{+\infty}\frac{\sin x}{x^{k}(1+x^{2})}dx \ $ via residue calculus

Published on 16 Apr 2026 - 8:35

161

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Improper integral with $-\infty$ and $+\infty$ as bounds

Published on 11 Apr 2026 - 21:27

1k

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Improper Integral $\int\limits_0^\frac{1}{2}x^n\cot(\pi x)\,dx$

Published on 16 Apr 2026 - 16:51

81

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Does $ \int x^{-2} \, \mathrm{d}{x} $ have a singularity?

Published on 19 Apr 2026 - 5:12

109

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Change of variables in $\int_{0}^{+\infty} \frac{x^{-\beta}}{1+x} \, dx$

Published on 15 Apr 2026 - 10:08

930

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Using Romberg integration with improper integral

Published on 12 Apr 2026 - 4:32

1.6k

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Why does Fubini's theorem not apply in this example?

Published on 11 Apr 2026 - 13:10

1k

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Improper Integral $\int\limits_0^{\frac12}(2x - 1)^6\log^2(2\sin\pi x)\,dx$

Published on 15 Apr 2026 - 20:17

78

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Proving an improper integral diverges

Published on 14 Apr 2026 - 14:43

101

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Showing that $\int_x^{\infty}\frac{1}{u^2}e^{(-u^2/2)}du=\frac{1}{x}e^{(-x^2/2)}-\int_x^{\infty}e^{{(-u^2/2)}}du$

Published on 16 Apr 2026 - 17:27

108

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Solve this improper integral: $\int_0^1 \ln{(x - 1)} \ dx$

Published on 16 Apr 2026 - 22:58

1.2k

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How to demonstrate the equality of these integral representations of $\pi$?

Published on 12 Apr 2026 - 6:04

78

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How to integrate this exponential function?

Published on 10 Apr 2026 - 15:25

3.7k

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Integral $\int_1^\infty\frac{dx}{1+2^x+3^x}$

Published on 16 Apr 2026 - 14:32

List Question

Show the integrals are alike without explicit computation.

$\int_{0}^{+\infty}\frac{\sin x}{x^{k}(1+x^{2})}dx \ $ via residue calculus

Improper integral with $-\infty$ and $+\infty$ as bounds

Improper Integral $\int\limits_0^\frac{1}{2}x^n\cot(\pi x)\,dx$

Does $ \int x^{-2} \, \mathrm{d}{x} $ have a singularity?

Change of variables in $\int_{0}^{+\infty} \frac{x^{-\beta}}{1+x} \, dx$

Using Romberg integration with improper integral

Why does Fubini's theorem not apply in this example?

Improper Integral $\int\limits_0^{\frac12}(2x - 1)^6\log^2(2\sin\pi x)\,dx$

Proving an improper integral diverges

Showing that $\int_x^{\infty}\frac{1}{u^2}e^{(-u^2/2)}du=\frac{1}{x}e^{(-x^2/2)}-\int_x^{\infty}e^{{(-u^2/2)}}du$

Solve this improper integral: $\int_0^1 \ln{(x - 1)} \ dx$

How to demonstrate the equality of these integral representations of $\pi$?

How to integrate this exponential function?

Integral $\int_1^\infty\frac{dx}{1+2^x+3^x}$

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