What is the integral from 0 to 2 of x^3(4+x^4)^3 ?

The integral from 0 to 2 of x^3(4+x^4)^3 is 9984

Popular >

integral from 0 to 2 of x^3(4+x^4)^3

\int_{0}^{2} x^{3} (4 + x^{4})^{3} d x

9984

Solution steps

\int_{0}^{2} x^{3} (4 + x^{4})^{3} d x

Expand

x^{3} (4 + x^{4})^{3} : 64 x^{3} + 48 x^{7} + 12 x^{11} + x^{15}

= \int_{0}^{2} 64 x^{3} + 48 x^{7} + 12 x^{11} + x^{15} 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} 64 x^{3} d x + \int_{0}^{2} 48 x^{7} d x + \int_{0}^{2} 12 x^{11} d x + \int_{0}^{2} x^{15} d x

\int_{0}^{2} 64 x^{3} d x = 256

\int_{0}^{2} 48 x^{7} d x = 1536

\int_{0}^{2} 12 x^{11} d x = 4096

\int_{0}^{2} x^{15} d x = 4096

= 256 + 1536 + 4096 + 4096

Simplify

= 9984

\int_{0}^{5} (x^{3}) d x

\int_{0}^{2} x (2 x - x^{2}) d x

\int_{0}^{π} - x cos (x) + x d x

\int_{1}^{e} 2 \frac{1}{x} d x

\int_{0}^{4} (- 2 x + 3) d x

What is the integral from 0 to 2 of x^3(4+x^4)^3 ?
The integral from 0 to 2 of x^3(4+x^4)^3 is 9984