What is the integral of (x^2-7)^2 ?

The integral of (x^2-7)^2 is (x^5)/5-(14x^3)/3+49x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x^2-7)^2

\int (x^{2} - 7)^{2} d x

\frac{x ^{5}}{5} - \frac{14 x ^{3}}{3} + 49 x + C

Solution steps

\int (x^{2} - 7)^{2} d x

Expand

(x^{2} - 7)^{2} : x^{4} - 14 x^{2} + 49

= \int x^{4} - 14 x^{2} + 49 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 14 x^{2} d x + \int 49 d x

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

\int 14 x^{2} d x = \frac{14 x ^{3}}{3}

\int 49 d x = 49 x

= \frac{x ^{5}}{5} - \frac{14 x ^{3}}{3} + 49 x

Add a constant to the solution

= \frac{x ^{5}}{5} - \frac{14 x ^{3}}{3} + 49 x + C

\int \frac{1}{( x - a ) ^{n}} d x

\int x^{2} 3^{2 x} d x

\int - x + 4 - x^{2} - 2 x d x

\int sec^{2} (x) (tan (x)) d x

\int \frac{x ^{3}}{1 - 36 x ^{8}} d x

What is the integral of (x^2-7)^2 ?
The integral of (x^2-7)^2 is (x^5)/5-(14x^3)/3+49x+C