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

The integral of (x^2-7)^2(2x) is (x^6)/3-7x^4+49x^2+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(2x)

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

\frac{x ^{6}}{3} - 7 x^{4} + 49 x^{2} + C

Solution steps

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

Take the constant out:

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

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

Expand

(x^{2} - 7)^{2} x : x^{5} - 14 x^{3} + 49 x

= 2 \cdot \int x^{5} - 14 x^{3} + 49 x 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

= 2 (\int x^{5} d x - \int 14 x^{3} d x + \int 49 x d x)

\int x^{5} d x = \frac{x ^{6}}{6}

\int 14 x^{3} d x = \frac{7 x ^{4}}{2}

\int 49 x d x = \frac{49 x ^{2}}{2}

= 2 (\frac{x ^{6}}{6} - \frac{7 x ^{4}}{2} + \frac{49 x ^{2}}{2})

Simplify

2 (\frac{x ^{6}}{6} - \frac{7 x ^{4}}{2} + \frac{49 x ^{2}}{2}) : \frac{x ^{6}}{3} - 7 x^{4} + 49 x^{2}

= \frac{x ^{6}}{3} - 7 x^{4} + 49 x^{2}

Add a constant to the solution

= \frac{x ^{6}}{3} - 7 x^{4} + 49 x^{2} + C

ln (\frac{5 x + 1}{x ^{2} - 3})

\frac{3}{x + 3}, at x = 4

y^{^{'}} = \frac{( x ^{3} + y ^{3} )}{3 x y ^{2}}

\frac{y}{x ^{2}} d x + (y - \frac{1}{x}) d y = 0

\frac{\partial}{\partial x} (e^{5 x yz - 9})

What is the integral of (x^2-7)^2(2x) ?
The integral of (x^2-7)^2(2x) is (x^6)/3-7x^4+49x^2+C