What is the integral from 0 to sqrt(2 of)x(x^2+1)^7 ?

The integral from 0 to sqrt(2 of)x(x^2+1)^7 is 410

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integral from 0 to sqrt(2 of)x(x^2+1)^7

\int_{0}^{2} x (x^{2} + 1)^{7} d x

410

Solution steps

\int_{0}^{2} x (x^{2} + 1)^{7} d x

Apply u-substitution

= \int_{1}^{3} \frac{u ^{7}}{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}^{3} u^{7} d u

Apply the Power Rule

= \frac{1}{2} [\frac{u ^{8}}{8}]_{1}^{3}

Compute the boundaries:

820

= \frac{1}{2} \cdot 820

Simplify

= 410

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What is the integral from 0 to sqrt(2 of)x(x^2+1)^7 ?
The integral from 0 to sqrt(2 of)x(x^2+1)^7 is 410