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

The integral of x^2cos(3x^3) is 1/9 sin(3x^3)+C

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

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

\frac{1}{9} sin (3 x^{3}) + C

Solution steps

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

Apply u-substitution

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

= \int \frac{cos ( 3 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 (3 u) d u

Apply u-substitution

: \int cos (v) \frac{1}{3} d v

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

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

Simplify

\frac{1}{3} \cdot \frac{1}{3} sin (3 x^{3}) : \frac{1}{9} sin (3 x^{3})

= \frac{1}{9} sin (3 x^{3})

Add a constant to the solution

= \frac{1}{9} sin (3 x^{3}) + C

\int 2 x e^{y} - y sin (x) d x

\int sin (0.01 x) d x

x^{(\frac{1}{2})}

\int x^{2} + 9^{2} d x

\int x 9 x - 10 d x

What is the integral of x^2cos(3x^3) ?
The integral of x^2cos(3x^3) is 1/9 sin(3x^3)+C