What is the integral of xcos(b)x ?

The integral of xcos(b)x is 1/3 x^3cos(b)+C

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integral of xcos(b)x

\int x cos (b) x d x

\frac{1}{3} x^{3} cos (b) + C

Solution steps

\int x cos (b) x d x

Take the constant out:

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

= cos (b) \cdot \int xx d x

Simplify

xx : x^{2}

= cos (b) \cdot \int x^{2} d x

Apply the Power Rule

= cos (b) \frac{x ^{3}}{3}

Simplify

cos (b) \frac{x ^{3}}{3} : \frac{1}{3} x^{3} cos (b)

= \frac{1}{3} x^{3} cos (b)

Add a constant to the solution

= \frac{1}{3} x^{3} cos (b) + C