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

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

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

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

sin (x^{3}) + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

= 3 \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

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

Use the common integral:

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

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

Substitute back

u = x^{3}

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

Simplify

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

= sin (x^{3})

Add a constant to the solution

= sin (x^{3}) + C

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