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

The integral of (x^2+5)^2 is (x^5)/5+(10x^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 (x^2+5)^2

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

\frac{x ^{5}}{5} + \frac{10 x ^{3}}{3} + 25 x + C

Solution steps

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

Expand

(x^{2} + 5)^{2} : x^{4} + 10 x^{2} + 25

= \int x^{4} + 10 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 x^{4} d x + \int 10 x^{2} d x + \int 25 d x

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

\int 10 x^{2} d x = \frac{10 x ^{3}}{3}

\int 25 d x = 25 x

= \frac{x ^{5}}{5} + \frac{10 x ^{3}}{3} + 25 x

Add a constant to the solution

= \frac{x ^{5}}{5} + \frac{10 x ^{3}}{3} + 25 x + C

x, 25

\int_{1}^{e} x \cdot ln (x) d x

2 sin (x), 4 cos (x)

\frac{d}{d x} (x tan (x))

\int \frac{1}{9 + 4 x ^{2}} d x

What is the integral of (x^2+5)^2 ?
The integral of (x^2+5)^2 is (x^5)/5+(10x^3)/3+25x+C