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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

= 2 \cdot \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

= 2 \cdot \frac{1}{3} \cdot \int cos (u) d u

Use the common integral:

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

= 2 \cdot \frac{1}{3} sin (u)

Substitute back

u = x^{3}

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

Simplify

2 \cdot \frac{1}{3} sin (x^{3}) : \frac{2}{3} sin (x^{3})

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

Add a constant to the solution

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

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