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

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

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integral of sin(y^3)y^2

\int sin (y^{3}) y^{2} d y

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

Solution steps

\int sin (y^{3}) y^{2} d y

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 = y^{3}

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

Simplify

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

Add a constant to the solution

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

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