Integration
in Calculus Answers by Level 1 User (140 points)

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sin^6x dx

From the reduction formula

Sin^n(x) = -(1/n)cosx.sin^(n - 2)x + {(n - 1)/n}∫sin^(n - 2)x dx

sin^6x = -(1/6)cosx.sin^4x + 5/6∫sin^4x dx

sin^6x = -1/6cosx.sin^4x + 5/6{ -1/4cosx.sin^2x + 3/4∫sin^2x dx}

= -1/6cosx.sin^4x - 5/24cosx.sin^2x + 5/8∫sin^2x dx

= -1/6cosx.sin^4x - 5/24cosx.sin^2x + 5/8{ x/2 - 1/4sin2x}

sin^6(x) = -1/6cosx.sin^4x - 5/24cosx.sin^2x -5/32sin2x + 5/16x + c

by Level 3 User (4.0k points)

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