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

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

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

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

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

Solution steps

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

Apply u-substitution

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

Use the common integral:

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

= \frac{1}{3} sin (u)

Substitute back

u = x^{3} + 3

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

Add a constant to the solution

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

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