trigints - Tricks for Trigonometric Integrals sinm x cosn x...

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Unformatted text preview: Tricks for Trigonometric Integrals sinm x cosn x dx m odd: = (1 - cos2 x)(m-1)/2 cosn x sin x dx = - (1 - u2 )(m-1)/2 un du n odd: = sinm x(1 - sin2 x)(n-1)/2 cos x dx = um (1 - u2 )(n-1)/2 du m, n both even: sin2 x = 1 (1 - cos 2x) 2 cos2 x = 1 (1 + cos 2x) 2 u = sin x u = cos x secm x tann x dx m even: = (tan2 x + 1)(m-2)/2 tann x sec2 x dx = (u2 + 1)(m-2)/2 un du n odd: = secm-1 x(sec2 x - 1)(n-1)/2 sec x tan x dx u = sec x = um-1 (u2 - 1)(n-1)/2 du m odd, n even: = = sinn x dx cosm+n x sinn x cos x dx (1 - sin2 x)(m+n+1)/2 u = tan x u = sin x and wait for "partial fractions" 1 sin(A + B) = sin A cos B + sin B cos A sin(A - B) = sin A cos B - sin B cos A cos(A + B) = cos A cos B - sin A sin B cos(A - B) = cos A cos B + sin A sin B 1 (sin(A + B) + sin(A - B)) 2 1 sin A sin B = (cos(A - B) - cos(A + B)) 2 1 cos A cos B = (cos(A - B) + cos(A + B)) 2 sin A cos B = 2 ...
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trigints - Tricks for Trigonometric Integrals sinm x cosn x...

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