What is the integral of x^ncos(a)x ?

The integral of x^ncos(a)x is 1/(n+2)x^{n+2}cos(a)+C

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integral of x^ncos(a)x

\int x^{n} cos (a) x d x

\frac{1}{n + 2} x^{n + 2} cos (a) + C

Solution steps

\int x^{n} cos (a) x d x

Take the constant out:

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

= cos (a) \cdot \int x^{n} x d x

Simplify

x^{n} x : x^{n + 1}

= cos (a) \cdot \int x^{n + 1} d x

Apply the Power Rule

: \frac{x ^{n + 2}}{n + 2}

= cos (a) \frac{x ^{n + 2}}{n + 2}

Simplify

cos (a) \frac{x ^{n + 2}}{n + 2} : \frac{1}{n + 2} x^{n + 2} cos (a)

= \frac{1}{n + 2} x^{n + 2} cos (a)

Add a constant to the solution

= \frac{1}{n + 2} x^{n + 2} cos (a) + C

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What is the integral of x^ncos(a)x ?
The integral of x^ncos(a)x is 1/(n+2)x^{n+2}cos(a)+C