# N even rewrite tan m x sec n x as tan m x sec n2 x

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Unformatted text preview: or ∫ a. n even: rewrite tan m x sec n x as tan m x sec n−2 x sec 2 x (then you can use 2 2 identity sec x = tan x + 1 ) m −1 n −1 b.m odd: rewrite as tan x sec x ⋅ sec x tan x (m-1 is even so can use 2 2 identity tan x = sec x − 1 ) tan m x using tan 2 x = sec 2 x − 1 c. m even and n odd: rewrite Examples: tan 3 ( x ) dx ∫ sec4 x dx ∫ sec4 x tan 2 x dx ∫ sec x ∫ tan 2 x dx ∫ tan 3 x dx ∫ sec 5 x tan x d x Integrals involving Sine-Cosine Products with Different Angles If you are given one of these where m ≠ n ∫ sin (mx )cos(nx )dx ∫ sin (mx )sin (nx )dx ∫ cos(mx )cos(nx )dx Use these formulas: 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 = ∫ cos(2x) sin(3x)dx Other formulas: 1 1 1. ∫ sin x dx = 2 x − 2 sin x cos x + C 2 2. cos 2 x dx = ∫ 1 1 x + sin x cos x + C 2 2 1 tan n x dx = tan n−1 x − ∫ tan n−2 xdx 3. ∫ n −1 n≥2 1 n−2 sec n x dx = sec n−2 x tan x + sec n−2 xdx 4. ∫ n −1 n −1 ∫ n≥2 Popper06 3. Compute ∫ sec ( 2x ) tan 3 ( 2x ) dx 4. Rewrite sin (5x) sin (3x) 5. ∫ sin ( 5 x ) sin ( 3 x ) dx =...
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