What is the integral of (x^2)sin(-x^3) ?

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

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integral of (x^2)sin(-x^3)

\int (x^{2}) sin (- x^{3}) d x

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

Solution steps

\int x^{2} sin (- x^{3}) d x

Simplify

x^{2} sin (- x^{3}) : - x^{2} sin (x^{3})

= \int - x^{2} sin (x^{3}) d x

Take the constant out:

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

= - \int x^{2} sin (x^{3}) d x

Apply u-substitution

: \int \frac{sin ( u )}{3} d u

= - \int \frac{sin ( u )}{3} d u

Take the constant out:

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

= - \frac{1}{3} \cdot \int sin (u) d u

Use the common integral:

\int sin (u) d u = - cos (u)

= - \frac{1}{3} (- cos (u))

Substitute back

u = x^{3}

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

Simplify

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

Add a constant to the solution

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

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