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

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

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integral of x^2sin(pix^3)

\int x^{2} sin (π x^{3}) d x

- \frac{1}{3 π} cos (π x^{3}) + C

Solution steps

\int x^{2} sin (π x^{3}) d x

Apply u-substitution

= \int \frac{sin ( u )}{3 π} d u

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{3 π} (- cos (u))

Substitute back

u = π x^{3}

= \frac{1}{3 π} (- cos (π x^{3}))

Simplify

= - \frac{1}{3 π} cos (π x^{3})

Add a constant to the solution

= - \frac{1}{3 π} cos (π x^{3}) + C

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