List questions from improper-integrals

Published on 17 May 2020 - 13:59

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Convergence of $\int_{-1}^{1} \frac{dx}{x\sqrt{1-x^2}}$

Published on 17 May 2020 - 17:55

204

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Prove the improper integral is absolutely convergent

Published on 26 Mar 2026 - 10:58

426

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Switching Limit and Integral in Improper Integral

Published on 18 May 2020 - 13:26

39

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For which $a$ does $f(x)=\frac{\arctan(x)}{\sqrt{x^a+x^{a+2}}}$ have finite volume?

Published on 18 May 2020 - 16:22

83

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Interval of p where $\int_0^\infty{\sqrt{x}\sin(\frac{1}{x^p})}dx$ converges

Published on 20 May 2020 - 5:30

230

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Evaluating $\int _0^{\infty }\frac{e^{-ax^m}-e^{-bx^n}}{x^p}\:dx$

Published on 20 May 2020 - 11:09

286

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What is a method for solving principal value integral of $\frac{1}{\pi}\int_{-B}^{B} \frac{x \sqrt{B^2-x^2}}{x-y}\mathrm{d} x$?

Published on 25 Mar 2026 - 19:06

139

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Divergence of definite integral

Published on 20 May 2020 - 18:44

178

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Proving that the Kernel of an Integral Equation is Weakly Singular

Published on 20 May 2020 - 20:59

101

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$ \lim_{t\to\infty}\int_{0}^{t}|g(s)|ds=0?$, when $\lim_{t\to\infty} |g(t)|=0$

Published on 21 May 2020 - 22:46

27

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One way to solve $\int_{0}^{\infty}3\Big(\frac{e^{-x^3}}{x+1}+\frac{xe^{-x^3}}{x^3+1}-\frac{e^{-x^3}}{x^3+1}\Big)dx=G$

Published on 25 Mar 2026 - 21:31

124

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Computing $\int_Q \frac{xy}{x^2+y^2}dxdy$

Published on 22 May 2020 - 9:16

288

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Efficient/faster methods to find the general closed form of $\int _0^1\frac{\ln \left(ax^2+b\right)}{x+1}\:dx$

Published on 22 May 2020 - 9:54

76

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Proving convergence of improper integral, g(t)

Published on 22 May 2020 - 15:29

List Question

Transforing improper integral into normal integral

Convergence of $\int_{-1}^{1} \frac{dx}{x\sqrt{1-x^2}}$

Prove the improper integral is absolutely convergent

Switching Limit and Integral in Improper Integral

For which $a$ does $f(x)=\frac{\arctan(x)}{\sqrt{x^a+x^{a+2}}}$ have finite volume?

Interval of p where $\int_0^\infty{\sqrt{x}\sin(\frac{1}{x^p})}dx$ converges

Evaluating $\int _0^{\infty }\frac{e^{-ax^m}-e^{-bx^n}}{x^p}\:dx$

What is a method for solving principal value integral of $\frac{1}{\pi}\int_{-B}^{B} \frac{x \sqrt{B^2-x^2}}{x-y}\mathrm{d} x$?

Divergence of definite integral

Proving that the Kernel of an Integral Equation is Weakly Singular

$ \lim_{t\to\infty}\int_{0}^{t}|g(s)|ds=0?$, when $\lim_{t\to\infty} |g(t)|=0$

One way to solve $\int_{0}^{\infty}3\Big(\frac{e^{-x^3}}{x+1}+\frac{xe^{-x^3}}{x^3+1}-\frac{e^{-x^3}}{x^3+1}\Big)dx=G$

Computing $\int_Q \frac{xy}{x^2+y^2}dxdy$

Efficient/faster methods to find the general closed form of $\int _0^1\frac{\ln \left(ax^2+b\right)}{x+1}\:dx$

Proving convergence of improper integral, g(t)

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