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

The integral of sin(2)x^2 is 1/3 sin(2)x^3+C

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integral of sin(2)x^2

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

\frac{1}{3} sin (2) x^{3} + C

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

= sin (2) \frac{x ^{3}}{3}

Simplify

sin (2) \frac{x ^{3}}{3} : \frac{1}{3} sin (2) x^{3}

= \frac{1}{3} sin (2) x^{3}

Add a constant to the solution

= \frac{1}{3} sin (2) x^{3} + C

\frac{d}{d x} (8 π x^{2})

f (x) = sin (x) cos (x) - x^{2}

\int x e^{- \frac{2}{5} x} d x

\int \frac{1}{( x - 1 ) ( x ^{2} + 1 )} d x

What is the integral of sin(2)x^2 ?
The integral of sin(2)x^2 is 1/3 sin(2)x^3+C