Asked by walter
what is the integral of sin^5(6x)dx
Answers
Answered by
Steve
first, note that if u = 6x, you have
1/6 ∫ sin^5 u du
= 1/6 ∫sin^4(u) sinu du
= -1/6 ∫(1-cos^2 u)^2 (-sinu du)
If v = cos u, then dv = -sinu du, and you have
-1/6 ∫(1-v^2)^2 dv
just expand that and it's a regular old polynomial.
1/6 ∫ sin^5 u du
= 1/6 ∫sin^4(u) sinu du
= -1/6 ∫(1-cos^2 u)^2 (-sinu du)
If v = cos u, then dv = -sinu du, and you have
-1/6 ∫(1-v^2)^2 dv
just expand that and it's a regular old polynomial.
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