What is the integral of xsin(a)x ?

The integral of xsin(a)x is 1/3 x^3sin(a)+C

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integral of xsin(a)x

\int x sin (a) x d x

\frac{1}{3} x^{3} sin (a) + C

Solution steps

\int x sin (a) x d x

Take the constant out:

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

= sin (a) \cdot \int xx d x

Simplify

xx : x^{2}

= sin (a) \cdot \int x^{2} d x

Apply the Power Rule

: \frac{x ^{3}}{3}

= sin (a) \frac{x ^{3}}{3}

Simplify

sin (a) \frac{x ^{3}}{3} : \frac{1}{3} x^{3} sin (a)

= \frac{1}{3} x^{3} sin (a)

Add a constant to the solution

= \frac{1}{3} x^{3} sin (a) + C

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