Integration of exsinx
NettetSimplify [Integrate [Sin [x]/Sqrt [1 + Tan [x]], x]] The result or solution obtained involves trigonometric functions as well as the incomplete elliptic integral of the first kind, … Nettet15. sep. 2024 · We may notice that the substitution x ↦ arcsin x, together with the Maclaurin series of arcsin 2, provides a further hypergeometric representation for the given integral: ∫ 0 π / 2 x sin n ( x) d x = ∫ 0 1 arcsin x 1 − x 2 x n d x = ∑ m ≥ 1 4 m 2 m ( 2 m + n) ( 2 m m) = 1 n + 2 ⋅ 3 F 2 ( 1, 1, 1 + n 2; 3 2, 2 + n 2; 1).
Integration of exsinx
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NettetDengan menggunakan rumus di atas, kita dapat menentukan koefisien deret Fourier a-2 dari sinyal X (t) = 2 sin wot sebagai berikut: a-2 = (1/T) * integral dari (T/2) ke (-T/2) [2 sin wot * cos (-2 * w0 * t)] dt + (1/T) * integral dari (T/2) ke … NettetIntegral (x*sin (x)/ (1 + cos (x)^2), (x, 0, pi)) The answer (Indefinite) [src] / / x*sin (x) x*sin (x) ----------- dx = C + ----------- dx 2 2 1 + cos (x) 1 + cos (x) / / ∫ x sin ( x) cos 2 ( x) + 1 d x = C + ∫ x sin ( x) cos 2 ( x) + 1 d x Simplify The answer [src]
Nettet14. apr. 2024 · Evaluate ∫ xsinx 1 + cos2xdx My attempt: I = ∫ xsinx 1 + cos2xdx = ∫x sinx 1 + cos2xdx = x∫ sinx 1 + cos2xdx − ∫[ d dxx∫ sinx 1 + cos2xdx]dx I ′ = ∫ sinx 1 + cos2xdx Let u = cosx ∴ du dx = − sinx du = ( − sinx)dx ∴ I ′ = − ∫ du 1 + u2 I ′ = − 1 1tan − 1(u 1) + C I ′ = − tan − 1(u) + C I ′ = − tan − 1(cosx) + C
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