What is the integral of x^2cos(x^3+4) ?

The integral of x^2cos(x^3+4) is 1/3 sin(x^3+4)+C

Popular >

integral of x^2cos(x^3+4)

\int x^{2} cos (x^{3} + 4) d x

\frac{1}{3} sin (x^{3} + 4) + C

Solution steps

\int x^{2} cos (x^{3} + 4) d x

Apply u-substitution

: \int \frac{u cos ( u ^{\frac{3}{2}} + 4 )}{2 x} d u

= \int \frac{cos ( u + 4 )}{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 + 4) d u

Apply u-substitution

: \int cos (v) d v

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

Use the common integral:

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

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

Substitute back

= \frac{1}{3} sin (x^{3} + 4)

Add a constant to the solution

= \frac{1}{3} sin (x^{3} + 4) + C

\int \frac{cos ( x )}{sin ( x ) + 1} d x

\int sec^{3} (p) tan (p) d p

\int \frac{3 + 4 x ^{\frac{3}{2}}}{x} d x

\int 1080 e^{- 0.9 x} d x

\int \frac{5 x - 5}{3 x ^{2} - 8 x - 3} d x

What is the integral of x^2cos(x^3+4) ?
The integral of x^2cos(x^3+4) is 1/3 sin(x^3+4)+C