List questions from definite-integrals

Published on 10 Apr 2026 - 20:01

747

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How to prove $\int \frac{1}{(x\sin(x))^2}\,dx$ doesnt have an elementary closed form?

Published on 09 Apr 2026 - 3:39

441

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Integration boundary condition dependent on integral derivative?

Published on 09 Apr 2026 - 3:36

170

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Calculating $\int^1_0\frac{x \log x}{1 + x^2} dx$

Published on 01 Mar 2018 - 9:27

79

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Find $\lim_{n \to \infty }\frac{x_{n+1}}{x_{n}}$

Published on 01 Mar 2018 - 9:54

61

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Check the convergence of $\sum\limits_{n=1}^\infty \int^r_0 \sin^n(x)\cos(x)\,\mathrm dx$ where $r>0$

Published on 01 Mar 2018 - 11:15

68

Views

Integrating trigonometric function

Published on 10 Apr 2026 - 17:46

65

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Finding value of $\int^{\pi}_{0}\frac{\sin^2(10x)}{\sin^2 (x)}dx$

Published on 01 Mar 2018 - 12:50

36

Views

Prove equation of two Integrals

Published on 01 Mar 2018 - 13:13

89

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Integral inequality $\int_{0}^{1}f^2\left(x\right)dx\geq\frac{3}{13}$

Published on 25 Mar 2026 - 1:20

236

Views

Integral with delta distribution kernel at singularity

Published on 11 Apr 2026 - 6:19

177

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Generalization of an Integral Trick?

Published on 10 Apr 2026 - 18:26

67

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Is the integral of $\frac{1}{x(x+1)}$ divergent?

Published on 25 Mar 2026 - 1:18

669

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Laplace's method to obtain the asymptotic approximation

Published on 24 Mar 2026 - 23:44

70

Views

Find the leading-order asymptotic approximation without using integration by part

Published on 24 Mar 2026 - 23:43

List Question

Integral finding - $u$-substitution

How to prove $\int \frac{1}{(x\sin(x))^2}\,dx$ doesnt have an elementary closed form?

Integration boundary condition dependent on integral derivative?

Calculating $\int^1_0\frac{x \log x}{1 + x^2} dx$

Find $\lim_{n \to \infty }\frac{x_{n+1}}{x_{n}}$

Check the convergence of $\sum\limits_{n=1}^\infty \int^r_0 \sin^n(x)\cos(x)\,\mathrm dx$ where $r>0$

Integrating trigonometric function

Finding value of $\int^{\pi}_{0}\frac{\sin^2(10x)}{\sin^2 (x)}dx$

Prove equation of two Integrals

Integral inequality $\int_{0}^{1}f^2\left(x\right)dx\geq\frac{3}{13}$

Integral with delta distribution kernel at singularity

Generalization of an Integral Trick?

Is the integral of $\frac{1}{x(x+1)}$ divergent?

Laplace's method to obtain the asymptotic approximation

Find the leading-order asymptotic approximation without using integration by part

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