What is the integral from 0 to 4 of xsqrt(x^2+5) ?

The integral from 0 to 4 of xsqrt(x^2+5) is 7sqrt(21)-(5sqrt(5))/3

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integral from 0 to 4 of xsqrt(x^2+5)

\int_{0}^{4} x x^{2} + 5 d x

721 - \frac{5 5}{3}

Decimal

28.35124 \dots

Solution steps

\int_{0}^{4} x x^{2} + 5 d x

Apply u-substitution

: \int_{5}^{21} u^{2} d u

= \int_{5}^{21} u^{2} d u

Apply the Power Rule

: [\frac{u ^{3}}{3}]_{5}^{21}

= [\frac{u ^{3}}{3}]_{5}^{21}

Compute the boundaries:

721 - \frac{5 5}{3}

= 721 - \frac{5 5}{3}

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What is the integral from 0 to 4 of xsqrt(x^2+5) ?
The integral from 0 to 4 of xsqrt(x^2+5) is 7sqrt(21)-(5sqrt(5))/3