What is the integral from 0 to 2 of x(x^2+1)^2 ?

The integral from 0 to 2 of x(x^2+1)^2 is 62/3

Popular >

integral from 0 to 2 of x(x^2+1)^2

\int_{0}^{2} x (x^{2} + 1)^{2} d x

\frac{62}{3}

Decimal

20.66666 \dots

Solution steps

\int_{0}^{2} x (x^{2} + 1)^{2} d x

Expand

x (x^{2} + 1)^{2} : x^{5} + 2 x^{3} + x

= \int_{0}^{2} x^{5} + 2 x^{3} + 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

= \int_{0}^{2} x^{5} d x + \int_{0}^{2} 2 x^{3} d x + \int_{0}^{2} x d x

\int_{0}^{2} x^{5} d x = \frac{32}{3}

\int_{0}^{2} 2 x^{3} d x = 8

\int_{0}^{2} x d x = 2

= \frac{32}{3} + 8 + 2

Simplify

\frac{32}{3} + 8 + 2 : \frac{62}{3}

= \frac{62}{3}

\int_{1}^{3} 4^{4 x} d x

\int_{2}^{4} \frac{1}{t t ^{2} - 4} d t

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

\int_{0}^{6} x e^{x^{2}} d x

\int_{1}^{9} \frac{6}{x} d x

What is the integral from 0 to 2 of x(x^2+1)^2 ?
The integral from 0 to 2 of x(x^2+1)^2 is 62/3