What is the integral of sin ^3 x.  

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to determine the value of Int [ (sin x)^3 dx]

Int [ (sin x)^3 dx]

=> Int [ (sin x)^2* sin x dx]

=> Int [ (1 – (cos x)^2 )* sin x dx]

let u = cos x => du = -sin x dx

=> Int [ (1 – u^2 )* (-du)]

=> u^3/3 – u + C

substitute u = cos x

=> ( cos x)^3 / 3 – cos x + C

The integral is (cos x)^3/ 3 – cos x + C

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