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

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

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

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

- \frac{1}{3} cos (x^{3}) + C

Solution steps

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

Apply u-substitution

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

= \int \frac{sin ( 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 sin (u) d u

Use the common integral:

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

= \frac{1}{3} (- cos (u))

Substitute back

u = x^{3}

= \frac{1}{3} (- cos (x^{3}))

Simplify

= - \frac{1}{3} cos (x^{3})

Add a constant to the solution

= - \frac{1}{3} cos (x^{3}) + C

\int \frac{x ^{3} - 1}{x + 2} d x

\frac{d}{d x} (sin (5 x))

x \to - 2 lim (4 x^{2 - 5 x + 2})

f (x) = 1 + 2 e^{x}, at x = 1

\int 4 x ln (x^{11}) d x

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