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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^3cos(x^4)

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

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

Solution steps

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

Apply u-substitution

: \int \frac{cos ( u )}{4} d u

= \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

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

Use the common integral:

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

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

Substitute back

u = x^{4}

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

Add a constant to the solution

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

\frac{\partial}{\partial x} (cos (e^{- x^{2}}))

\frac{d}{d x} (x^{10} - 1)

\frac{d}{d x} (4 x^{2} - x^{3})

\int 4 x d x

\int 6 x^{- 3} d x

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