Determine the antiderivative of y=sin x*cos^n x?

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We have to find the anti derivative of y = sin x*(cos x)^n

let cos x = y

=> dy/dx = -sin x

=> (-1)*dy = sin x dx

Int [ sin x*(cos x)^n dx]

=> Int [ (-1)* y^n]

=> (-1)* y^(n+1) / (n + 1)

substitute y =...

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We have to find the anti derivative of y = sin x*(cos x)^n

let cos x = y

=> dy/dx = -sin x

=> (-1)*dy = sin x dx

Int [ sin x*(cos x)^n dx]

=> Int [ (-1)* y^n]

=> (-1)* y^(n+1) / (n + 1)

substitute y = cos x

=> [-1/(n+1)]*(cos x)^(n+1)

The required anti derivative is [-1/(n+1)]*(cos x)^(n+1)

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