Question

How to evaluate $\frac{1}{2\pi}\int \frac{1}{(1-\alpha \cos \omega)^2 +\alpha^2\sin^2 \omega } \, d\omega$

score 77 · Answer 1 · 2026-03-21 21:19:40

77

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How to evaluate $\frac{1}{2\pi}\int \frac{1}{(1-\alpha \cos \omega)^2 +\alpha^2\sin^2 \omega } \, d\omega$

Published on 21 Mar 2026 - 21:19

score 142 · Answer 2 · 2026-03-24 23:42:32

142

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Types of trigonometric integrals

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score 132 · Answer 3 · 2026-03-23 06:02:13

132

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How to calculate $\int_{ }^{ }\frac{14x+2}{x^2+4}dx$

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score 761 · Answer 4 · 2026-03-25 06:19:16

761

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score 106 · Answer 5 · 2026-03-22 03:06:27

106

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Closed form for:$I(j) = \int_0^1 \dfrac{\cos{(\pi j x/2)}}{\sin{(\frac{\pi}{4}(1-x))}} \log{\Big( \frac{\sin{\pi /4}}{\sin{\pi x/4}} \Big)}dx$?

Published on 22 Mar 2026 - 3:06

score 304 · Answer 6 · 2026-03-20 07:53:20

304

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score 191 · Answer 7 · 2026-03-25 11:13:38

191

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Computing $\lim\limits_{n \to \infty} \int_0^{\frac{\pi}{2}}{\frac{(\sin(x))^{n}}{1-\sin{(x)}}\,\mathrm{d}x} $

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score 148 · Answer 8 · 2026-03-25 20:13:48

148

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Computing $\lim_{n \rightarrow \infty} \int_{0}^{\pi/3} \frac{\sin^{n}x}{\sin^{n}x+\cos^{n}x}dx$ using Dominated Convergence Theorem

Published on 25 Mar 2026 - 20:13

score 181 · Answer 9 · 2026-03-22 01:54:49

181

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Compute $\lim_{n \to \infty} \int_0^{\frac{\pi}{2}} \sum_{k=1}^n (\sin{x})^kdx$

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score 141 · Answer 10 · 2026-03-22 09:38:00

141

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score 239 · Answer 11 · 2026-03-21 17:56:40

239

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Evaluating $\lim\limits_{h\to 0^+} \frac1h(\int_{0}^{\pi}\sin^{h}x~{\rm d}x-\pi)$

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score 68 · Answer 12 · 2026-03-22 12:29:46

68

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score 547 · Answer 13 · 2026-03-22 08:45:20

547

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Strange Trig Substitution in Integral

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score 97 · Answer 14 · 2026-03-19 23:51:45

97

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definite integration of a trigonometric function with branch cut

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score 516 · Answer 15 · 2026-03-25 07:48:42

516

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An interesting integral $\cos(x)\cos(x^2)\cos(x^3)...$

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List Question

How to evaluate $\frac{1}{2\pi}\int \frac{1}{(1-\alpha \cos \omega)^2 +\alpha^2\sin^2 \omega } \, d\omega$

Types of trigonometric integrals

How to calculate $\int_{ }^{ }\frac{14x+2}{x^2+4}dx$

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