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

The integral of x^2cos(2x^3) is 1/6 sin(2x^3)+C

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integral of x^2cos(2x^3)

\int x^{2} cos (2 x^{3}) d x

\frac{1}{6} sin (2 x^{3}) + C

Solution steps

\int x^{2} cos (2 x^{3}) d x

Apply u-substitution

: \int \frac{cos ( u )}{6} d u

= \int \frac{cos ( u )}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{6} sin (u)

Substitute back

u = 2 x^{3}

= \frac{1}{6} sin (2 x^{3})

Add a constant to the solution

= \frac{1}{6} sin (2 x^{3}) + C

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What is the integral of x^2cos(2x^3) ?
The integral of x^2cos(2x^3) is 1/6 sin(2x^3)+C