What is the integral of 1/2 xsin(4)x^2 ?

The integral of 1/2 xsin(4)x^2 is 1/8 sin(4)x^4+C

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integral of 1/2 xsin(4)x^2

\int \frac{1}{2} x sin (4) x^{2} d x

\frac{1}{8} sin (4) x^{4} + C

Solution steps

\int \frac{1}{2} x sin (4) x^{2} d x

Take the constant out:

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

= \frac{1}{2} sin (4) \cdot \int x x^{2} d x

Simplify

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

= \frac{1}{2} sin (4) \cdot \int x^{3} d x

Apply the Power Rule

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

= \frac{1}{2} sin (4) \frac{x ^{4}}{4}

Simplify

\frac{1}{2} sin (4) \frac{x ^{4}}{4} : \frac{1}{8} sin (4) x^{4}

= \frac{1}{8} sin (4) x^{4}

Add a constant to the solution

= \frac{1}{8} sin (4) x^{4} + C

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What is the integral of 1/2 xsin(4)x^2 ?
The integral of 1/2 xsin(4)x^2 is 1/8 sin(4)x^4+C