What is the integral from 0 to 2 of x(x^2+1)^5 ?

The integral from 0 to 2 of x(x^2+1)^5 is 1302

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integral from 0 to 2 of x(x^2+1)^5

\int_{0}^{2} x (x^{2} + 1)^{5} d x

1302

Solution steps

\int_{0}^{2} x (x^{2} + 1)^{5} d x

Apply u-substitution

= \int_{1}^{5} \frac{u ^{5}}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{1}^{5} u^{5} d u

Apply the Power Rule

= \frac{1}{2} [\frac{u ^{6}}{6}]_{1}^{5}

Compute the boundaries:

2604

= \frac{1}{2} \cdot 2604

Simplify

= 1302

What is the integral from 0 to 2 of x(x^2+1)^5 ?
The integral from 0 to 2 of x(x^2+1)^5 is 1302