Question

Methods to solve $\int_{0}^{\infty} x^{n}\cos(x)\:dx$

score 496 · Answer 1 · 2026-04-16 11:31:11

496

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Methods to solve $\int_{0}^{\infty} x^{n}\cos(x)\:dx$

Published on 16 Apr 2026 - 11:31

score 457 · Answer 2 · 2026-04-14 02:52:26

457

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Why does this method fail for finding the Fourier series for $\cos\left(\frac{x}{2}\right)$ on the interval $-\pi \lt x \lt \pi$?

Published on 14 Apr 2026 - 2:52

score 69 · Answer 3 · 2026-04-16 11:59:13

69

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$\int_0^x\sin^at\cos^bt\, \mathrm{d}t=?$

Published on 16 Apr 2026 - 11:59

score 222 · Answer 4 · 2026-05-11 01:13:04

222

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Showing $\int_0^{\int_0^u{\rm sech}vdv}\sec vdv\equiv u$ and $\int_0^{\int_0^u\sec vdv}{\rm sech} vdv\equiv u$

Published on 11 May 2026 - 1:13

score 751 · Answer 5 · 2026-04-17 12:18:28

751

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Evaluate $I_n = \int_0^{\pi / 2} \sin n \theta \cos \theta \,d\theta$ by integrating by parts twice

Published on 17 Apr 2026 - 12:18

score 59 · Answer 6 · 2026-04-17 09:41:12

59

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Contour intergal of a rational trigonometric function, can't find my mistake.

Published on 17 Apr 2026 - 9:41

score 185 · Answer 7 · 2026-04-13 07:15:52

185

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Can these integrals be solved by u-substitution using trig identities?

Published on 13 Apr 2026 - 7:15

score 72 · Answer 8 · 2026-04-17 11:40:29

72

Views

About $ f(w,L) = \int_1^w \int_0^{2 L \pi} \frac{ \ln(\frac{\sin(x) +\ sin(vx)}{2} + \frac{5}{4})}{L(w - 1)} dx dv $

Published on 17 Apr 2026 - 11:40

score 857 · Answer 9 · 2026-04-12 12:47:00

857

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Calculate the integral of $\frac {\exp(z)}{\sin(z)}$ over $|z|=4$ using the residue theorem.

Published on 12 Apr 2026 - 12:47

score 50 · Answer 10 · 2026-04-15 19:01:37

50

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Calculation of $\int_{-R}^R(R-x^2)^\frac{n-1}{2}dx$

Published on 15 Apr 2026 - 19:01

score 53 · Answer 11 · 2026-04-12 02:45:49

53

Views

A trigonometric function question for calculus

Published on 12 Apr 2026 - 2:45

score 234 · Answer 12 · 2026-04-16 18:52:01

234

Views

Prove that $\int_0^{\frac{n\pi}{4}} \frac{1}{3\sin^4(x) + 3\cos^4(x) -1} dx = \frac{n\pi}{4} $

Published on 16 Apr 2026 - 18:52

score 199 · Answer 13 · 2026-04-15 21:08:17

199

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Integral $\int_{0}^{\infty}\frac{1}{x^2}(\frac{1}{\cosh^2x}-\frac{\tanh{x}}{x})dx$

Published on 15 Apr 2026 - 21:08

score 89 · Answer 14 · 2026-04-11 03:29:15

89

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How do I integrate $\sqrt{1+\sec2x}$?

Published on 11 Apr 2026 - 3:29

score 54 · Answer 15 · 2026-04-16 05:37:38

54

Views

Integral $\cos\left(\ln\left(e^t+1\right)+at+b\right)dt$

Published on 16 Apr 2026 - 5:37

List Question

Methods to solve $\int_{0}^{\infty} x^{n}\cos(x)\:dx$

Why does this method fail for finding the Fourier series for $\cos\left(\frac{x}{2}\right)$ on the interval $-\pi \lt x \lt \pi$?

$\int_0^x\sin^at\cos^bt\, \mathrm{d}t=?$

Showing $\int_0^{\int_0^u{\rm sech}vdv}\sec vdv\equiv u$ and $\int_0^{\int_0^u\sec vdv}{\rm sech} vdv\equiv u$

Evaluate $I_n = \int_0^{\pi / 2} \sin n \theta \cos \theta \,d\theta$ by integrating by parts twice

Contour intergal of a rational trigonometric function, can't find my mistake.

Can these integrals be solved by u-substitution using trig identities?

About $ f(w,L) = \int_1^w \int_0^{2 L \pi} \frac{ \ln(\frac{\sin(x) +\ sin(vx)}{2} + \frac{5}{4})}{L(w - 1)} dx dv $

Calculate the integral of $\frac {\exp(z)}{\sin(z)}$ over $|z|=4$ using the residue theorem.

Calculation of $\int_{-R}^R(R-x^2)^\frac{n-1}{2}dx$

A trigonometric function question for calculus

Prove that $\int_0^{\frac{n\pi}{4}} \frac{1}{3\sin^4(x) + 3\cos^4(x) -1} dx = \frac{n\pi}{4} $

Integral $\int_{0}^{\infty}\frac{1}{x^2}(\frac{1}{\cosh^2x}-\frac{\tanh{x}}{x})dx$

How do I integrate $\sqrt{1+\sec2x}$?

Integral $\cos\left(\ln\left(e^t+1\right)+at+b\right)dt$

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