What is the integral of 2x(8x^2-20)^2 ?

The integral of 2x(8x^2-20)^2 is 2((32x^6)/3-80x^4+200x^2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2x(8x^2-20)^2

\int 2 x (8 x^{2} - 20)^{2} d x

2 (\frac{32 x ^{6}}{3} - 80 x^{4} + 200 x^{2}) + C

Solution steps

\int 2 x (8 x^{2} - 20)^{2} d x

Take the constant out:

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

= 2 \cdot \int x (8 x^{2} - 20)^{2} d x

Expand

x (8 x^{2} - 20)^{2} : 64 x^{5} - 320 x^{3} + 400 x

= 2 \cdot \int 64 x^{5} - 320 x^{3} + 400 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 64 x^{5} d x - \int 320 x^{3} d x + \int 400 x d x)

\int 64 x^{5} d x = \frac{32 x ^{6}}{3}

\int 320 x^{3} d x = 80 x^{4}

\int 400 x d x = 200 x^{2}

= 2 (\frac{32 x ^{6}}{3} - 80 x^{4} + 200 x^{2})

Add a constant to the solution

= 2 (\frac{32 x ^{6}}{3} - 80 x^{4} + 200 x^{2}) + C

x \to 1 + lim (1 + \frac{1}{x - 1})

\int 7 x + 5 d x

f (x) = sin (x^{5})

x \to - 2 lim (\frac{1}{( 2 + x ) ^{3}})

\int 13 x sin (x) d x

What is the integral of 2x(8x^2-20)^2 ?
The integral of 2x(8x^2-20)^2 is 2((32x^6)/3-80x^4+200x^2)+C