What is the integral of (4x^2+5)^2 ?

The integral of (4x^2+5)^2 is (16x^5)/5+(40x^3)/3+25x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (4x^2+5)^2

\int (4 x^{2} + 5)^{2} d x

\frac{16 x ^{5}}{5} + \frac{40 x ^{3}}{3} + 25 x + C

Solution steps

\int (4 x^{2} + 5)^{2} d x

Expand

(4 x^{2} + 5)^{2} : 16 x^{4} + 40 x^{2} + 25

= \int 16 x^{4} + 40 x^{2} + 25 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 16 x^{4} d x + \int 40 x^{2} d x + \int 25 d x

\int 16 x^{4} d x = \frac{16 x ^{5}}{5}

\int 40 x^{2} d x = \frac{40 x ^{3}}{3}

\int 25 d x = 25 x

= \frac{16 x ^{5}}{5} + \frac{40 x ^{3}}{3} + 25 x

Add a constant to the solution

= \frac{16 x ^{5}}{5} + \frac{40 x ^{3}}{3} + 25 x + C

\int 8 - 3 x d x

\int x^{2} e^{2 x^{3} + 4} d x

\int \frac{x}{x ^{2} + 10} d x

\int \frac{2}{( 2 x - 3 ) ln ( 2 x - 3 )} d x

\int - z e^{- yz} d y

What is the integral of (4x^2+5)^2 ?
The integral of (4x^2+5)^2 is (16x^5)/5+(40x^3)/3+25x+C