Question

Prove $\int_0^\pi\frac{\cos(n\theta)}{\cos\theta - \cos\theta_0}d\theta = \frac{\pi\sin(n\theta_0)}{\sin\theta_0}$

score 213 · Answer 1 · 2026-04-16 07:29:19

213

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Prove $\int_0^\pi\frac{\cos(n\theta)}{\cos\theta - \cos\theta_0}d\theta = \frac{\pi\sin(n\theta_0)}{\sin\theta_0}$

Published on 16 Apr 2026 - 7:29

score 56 · Answer 2 · 2026-04-17 04:45:52

56

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solve $\int_{-\sqrt{3}}^{\sqrt{3}} 4 \sqrt{3-y^2}dy$

Published on 17 Apr 2026 - 4:45

score 91 · Answer 3 · 2026-04-16 00:41:51

91

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Finding $\int\frac{\sin x+\tan x}{\cos x+\csc x}dx$

Published on 16 Apr 2026 - 0:41

score 1.7k · Answer 4 · 2026-04-15 14:19:21

1.7k

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Trig Subsitution When There's No Square Root

Published on 15 Apr 2026 - 14:19

score 75 · Answer 5 · 2026-04-15 08:28:00

75

Views

Proof that $\frac{2\times2\times2\times4\times4\cdots(2n)\times(2n)}{3\times3\times5\times5\cdots(2n-1)\times(2n+1)}$ converges to $\frac{\pi}{2}$

Published on 15 Apr 2026 - 8:28

score 71 · Answer 6 · 2026-04-14 13:20:15

71

Views

Does $-\frac12\cos(2x)=\sin^2(x)$?

Published on 14 Apr 2026 - 13:20

score 100 · Answer 7 · 2026-05-11 04:10:39

100

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Closed form solution to $\int_0^{\pi/4}\frac{e^{ic\sqrt{1+ br^2(\theta)}}}{\sqrt{1+ br^2(\theta)}}\,d\theta$

Published on 11 May 2026 - 4:10

score 115 · Answer 8 · 2026-04-16 01:23:17

115

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Integrate $\int \frac{\cos^2 x}{(1 - \cos x)\sin x} dx$

Published on 16 Apr 2026 - 1:23

score 78 · Answer 9 · 2026-04-16 10:21:59

78

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How do I justify the convergence of :$\int_{-\infty}^{+\infty}\dfrac{\exp(-x^{2n+1}\arctan (x))}{1+x^{2n}}dx$ with $n$ a positive integer?

Published on 16 Apr 2026 - 10:21

score 236 · Answer 10 · 2026-04-16 11:54:32

236

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Prove $\int^{\infty}_{0} \frac{\cos(ax)}{\cosh(\beta x)}dx = \frac{\pi}{2\beta}\operatorname{sech}(\frac{a\pi}{2\beta})$

Published on 16 Apr 2026 - 11:54

score 43 · Answer 11 · 2026-04-14 00:29:19

43

Views

Trigonometric integrals involving tangent

Published on 14 Apr 2026 - 0:29

score 75 · Answer 12 · 2026-04-13 13:51:49

75

Views

Definite integral of the sum of quadratics in sine and cosine raised to a negative power

Published on 13 Apr 2026 - 13:51

score 131 · Answer 13 · 2026-04-16 12:53:54

131

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Evaluation of $\int_{1}^{\infty} \frac{\arctan (x+1)}{x^2+4} dx$ in closed form?

Published on 16 Apr 2026 - 12:53

score 1.3k · Answer 14 · 2026-04-15 23:00:59

1.3k

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show $\int \frac{1}{\cosh(x)}dx = \arctan(\sinh(x))$ using the substitution $u=\sinh(x)$

Published on 15 Apr 2026 - 23:00

score 208 · Answer 15 · 2026-04-15 10:47:24

208

Views

Series of Beta Function

Published on 15 Apr 2026 - 10:47

List Question

Prove $\int_0^\pi\frac{\cos(n\theta)}{\cos\theta - \cos\theta_0}d\theta = \frac{\pi\sin(n\theta_0)}{\sin\theta_0}$

solve $\int_{-\sqrt{3}}^{\sqrt{3}} 4 \sqrt{3-y^2}dy$

Finding $\int\frac{\sin x+\tan x}{\cos x+\csc x}dx$

Trig Subsitution When There's No Square Root

Proof that $\frac{2\times2\times2\times4\times4\cdots(2n)\times(2n)}{3\times3\times5\times5\cdots(2n-1)\times(2n+1)}$ converges to $\frac{\pi}{2}$

Does $-\frac12\cos(2x)=\sin^2(x)$?

Closed form solution to $\int_0^{\pi/4}\frac{e^{ic\sqrt{1+ br^2(\theta)}}}{\sqrt{1+ br^2(\theta)}}\,d\theta$

Integrate $\int \frac{\cos^2 x}{(1 - \cos x)\sin x} dx$

How do I justify the convergence of :$\int_{-\infty}^{+\infty}\dfrac{\exp(-x^{2n+1}\arctan (x))}{1+x^{2n}}dx$ with $n$ a positive integer?

Prove $\int^{\infty}_{0} \frac{\cos(ax)}{\cosh(\beta x)}dx = \frac{\pi}{2\beta}\operatorname{sech}(\frac{a\pi}{2\beta})$

Trigonometric integrals involving tangent

Definite integral of the sum of quadratics in sine and cosine raised to a negative power

Evaluation of $\int_{1}^{\infty} \frac{\arctan (x+1)}{x^2+4} dx$ in closed form?

show $\int \frac{1}{\cosh(x)}dx = \arctan(\sinh(x))$ using the substitution $u=\sinh(x)$

Series of Beta Function

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