en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2x)^4

Solution

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

Solution

\frac{16 x ^{5}}{5} + C

Solution steps

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

Simplify

(2 x)^{4} : 16 x^{4}

= \int 16 x^{4} d x

Take the constant out:

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

= 16 \cdot \int x^{4} d x

Apply the Power Rule

: \frac{x ^{5}}{5}

= 16 \cdot \frac{x ^{5}}{5}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{16 x ^{5}}{5}

Add a constant to the solution

= \frac{16 x ^{5}}{5} + C

Popular Examples

integral of (inx)/(x^3)

\int \frac{in x}{x ^{3}} d x

integral of x^4(x^5-7)^5

\int x^{4} (x^{5} - 7)^{5} d x

integral of sin(x)In(cos(x))

\int sin (x) I n (cos (x)) d x

integral of 3/((x-7)(x-4))

\int \frac{3}{( x - 7 ) ( x - 4 )} d x

integral of 3x^5-8x^3+2

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

Frequently Asked Questions (FAQ)

What is the integral of (2x)^4 ?
The integral of (2x)^4 is (16x^5)/5+C