What is the integral of 6x^2cos(x^3) ?

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

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integral of 6x^2cos(x^3)

\int 6 x^{2} cos (x^{3}) d x

2 sin (x^{3}) + C

Solution steps

\int 6 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

= 6 \cdot \int x^{2} cos (x^{3}) d x

Apply u-substitution

: \int \frac{cos ( u )}{3} d u

= 6 \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

= 6 \cdot \frac{1}{3} \cdot \int cos (u) d u

Use the common integral:

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

= 6 \cdot \frac{1}{3} sin (u)

Substitute back

u = x^{3}

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

Simplify

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

= 2 sin (x^{3})

Add a constant to the solution

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

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