What is the integral of sin(x)cos^4(x ?

The integral of sin(x)cos^4(x is cos^4(d)(-xcos(x)+sin(x))+C

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integral of sin(x)cos^4(x

\int sin (x) cos^{4} (d) x d x

cos^{4} (d) (- x cos (x) + sin (x)) + C

Solution steps

\int sin (x) cos^{4} (d) x d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= cos^{4} (d) \cdot \int sin (x) x d x

Apply Integration By Parts

= cos^{4} (d) (- x cos (x) - \int - cos (x) d x)

\int - cos (x) d x = - sin (x)

= cos^{4} (d) (- x cos (x) - (- sin (x)))

Simplify

= cos^{4} (d) (- x cos (x) + sin (x))

Add a constant to the solution

= cos^{4} (d) (- x cos (x) + sin (x)) + C

What is the integral of sin(x)cos^4(x ?
The integral of sin(x)cos^4(x is cos^4(d)(-xcos(x)+sin(x))+C