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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

\frac{1}{2} sin (x^{4}) + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

= 2 \cdot \int \frac{cos ( u )}{4} d u

Take the constant out:

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

= 2 \cdot \frac{1}{4} \cdot \int cos (u) d u

Use the common integral:

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

= 2 \cdot \frac{1}{4} sin (u)

Substitute back

u = x^{4}

= 2 \cdot \frac{1}{4} sin (x^{4})

Simplify

2 \cdot \frac{1}{4} sin (x^{4}) : \frac{1}{2} sin (x^{4})

= \frac{1}{2} sin (x^{4})

Add a constant to the solution

= \frac{1}{2} sin (x^{4}) + C

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