What is the integral of x^2sin(n)x ?

The integral of x^2sin(n)x is 1/4 x^4sin(n)+C

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integral of x^2sin(n)x

\int x^{2} sin (n) x d x

\frac{1}{4} x^{4} sin (n) + C

Solution steps

\int x^{2} sin (n) x d x

Take the constant out:

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

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

Simplify

x^{2} x : x^{3}

= sin (n) \cdot \int x^{3} d x

Apply the Power Rule

: \frac{x ^{4}}{4}

= sin (n) \frac{x ^{4}}{4}

Simplify

sin (n) \frac{x ^{4}}{4} : \frac{1}{4} x^{4} sin (n)

= \frac{1}{4} x^{4} sin (n)

Add a constant to the solution

= \frac{1}{4} x^{4} sin (n) + C

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What is the integral of x^2sin(n)x ?
The integral of x^2sin(n)x is 1/4 x^4sin(n)+C