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

The integral of x^2sin(x^3)cos(x^3) is -1/12 cos(2x^3)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

- \frac{1}{12} cos (2 x^{3}) + C

Solution steps

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

Rewrite using trig identities

= \int \frac{1}{2} x^{2} sin (2 x^{3}) d x

Take the constant out:

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

= \frac{1}{2} \cdot \int x^{2} sin (2 x^{3}) d x

Apply u-substitution

: \int \frac{sin ( u )}{6} d u

= \frac{1}{2} \cdot \int \frac{sin ( u )}{6} d u

Take the constant out:

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

= \frac{1}{2} \cdot \frac{1}{6} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{2} \cdot \frac{1}{6} (- cos (u))

Substitute back

u = 2 x^{3}

= \frac{1}{2} \cdot \frac{1}{6} (- cos (2 x^{3}))

Simplify

\frac{1}{2} \cdot \frac{1}{6} (- cos (2 x^{3})) : - \frac{1}{12} cos (2 x^{3})

= - \frac{1}{12} cos (2 x^{3})

Add a constant to the solution

= - \frac{1}{12} cos (2 x^{3}) + C

- cos (x)

\int 1.2 x e^{7 x^{2}} d x

\int (e^{5} - 3^{e}) d x

\int 10 e^{10 x} d x

\int sin (0.5 x) d x

What is the integral of x^2sin(x^3)cos(x^3) ?
The integral of x^2sin(x^3)cos(x^3) is -1/12 cos(2x^3)+C