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

The integral of (2x+3)^4 is 1/10 (2x+3)^5+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (2x+3)^4

integral

(2 x + 3)^{4}

\frac{1}{10} (2 x + 3)^{5} + C

Solution steps

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

Apply u-substitution

= \int \frac{u ^{4}}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int u^{4} d u

Apply the Power Rule

= \frac{1}{2} \cdot \frac{u ^{5}}{5}

Substitute back

u = 2 x + 3

= \frac{1}{2} \cdot \frac{( 2 x + 3 ) ^{5}}{5}

Simplify

\frac{1}{2} \cdot \frac{( 2 x + 3 ) ^{5}}{5} : \frac{1}{10} (2 x + 3)^{5}

= \frac{1}{10} (2 x + 3)^{5}

Add a constant to the solution

= \frac{1}{10} (2 x + 3)^{5} + C