List questions from definite-integrals

Published on 12 Apr 2026 - 6:54

152

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Evaluate $\int_1^{\infty} \frac {(\{x\}-\frac 12)dx}{x}$

Published on 17 Apr 2026 - 12:18

292

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Integrating $\frac{\arctan x}{x\sqrt{\smash[b]{1-x^2}}}$

Published on 17 Apr 2026 - 5:05

232

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Proving $\int_0^\infty\frac{e^x-1}{x(e^x+1)^2}dx=6\ln A-\frac12-\frac16\ln2-\frac12\ln\pi$

Published on 17 Apr 2026 - 1:25

53

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Laplace transform $f(t)f'(t)$

Published on 16 Apr 2026 - 19:42

162

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Evaluation of $\int_0^T \int_0^t \tau^{-1/2} (T-\tau)^{-1/2} \exp(\frac{ix^2}{2(T-\tau)})d\tau dt$

Published on 18 Apr 2026 - 5:36

128

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is $\int_{-1}^{1} dsgn = 2?$

Published on 14 Apr 2026 - 3:55

317

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Calculate $\int_{1}^{-1} |z-1|^2 dz$ along the upper half of the circle $|z|=1$

Published on 15 Apr 2026 - 17:11

77

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Why is the integration $\int_{\frac6\pi}^{\frac2{3\pi}}\frac{\cos\left(\frac1x\right)}{x^2}dx$ non-negative?

Published on 15 Apr 2026 - 18:25

208

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Compute $\int_0^2\frac {\arctan{x}}{x^2+2x+2}dx$

Published on 17 Apr 2026 - 11:48

37

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Definite integral: putting value before integration

Published on 12 Apr 2026 - 3:53

254

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Triple Integrals in Spherical Coordinates, problem with boundaries

Published on 25 Mar 2026 - 4:54

61

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Proving a constant to the power of a constant is bigger than another constant

Published on 10 Apr 2026 - 13:29

2.5k

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Orthogonality Relations for $\sin kx$ and $\cos nx$ for arbitrary domains

Published on 15 Apr 2026 - 18:43

85

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Integration bounds in triple integrals

Published on 12 Apr 2026 - 7:56

List Question

Puzzling Double integral

Evaluate $\int_1^{\infty} \frac {(\{x\}-\frac 12)dx}{x}$

Integrating $\frac{\arctan x}{x\sqrt{\smash[b]{1-x^2}}}$

Proving $\int_0^\infty\frac{e^x-1}{x(e^x+1)^2}dx=6\ln A-\frac12-\frac16\ln2-\frac12\ln\pi$

Laplace transform $f(t)f'(t)$

Evaluation of $\int_0^T \int_0^t \tau^{-1/2} (T-\tau)^{-1/2} \exp(\frac{ix^2}{2(T-\tau)})d\tau dt$

is $\int_{-1}^{1} dsgn = 2?$

Calculate $\int_{1}^{-1} |z-1|^2 dz$ along the upper half of the circle $|z|=1$

Why is the integration $\int_{\frac6\pi}^{\frac2{3\pi}}\frac{\cos\left(\frac1x\right)}{x^2}dx$ non-negative?

Compute $\int_0^2\frac {\arctan{x}}{x^2+2x+2}dx$

Definite integral: putting value before integration

Triple Integrals in Spherical Coordinates, problem with boundaries

Proving a constant to the power of a constant is bigger than another constant

Orthogonality Relations for $\sin kx$ and $\cos nx$ for arbitrary domains

Integration bounds in triple integrals

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