What is the integral from 0 to 4 of xsqrt(x^2+7) ?

The integral from 0 to 4 of xsqrt(x^2+7) is (23sqrt(23)-7sqrt(7))/3

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integral from 0 to 4 of xsqrt(x^2+7)

\int_{0}^{4} x x^{2} + 7 d x

\frac{23 23 - 7 7}{3}

Decimal Notation

30.59462 \dots

Solution steps

\int_{0}^{4} x x^{2} + 7 d x

Apply u-substitution

: \int_{7}^{23} u^{2} d u

= \int_{7}^{23} u^{2} d u

Apply the Power Rule

: [\frac{u ^{3}}{3}]_{7}^{23}

= [\frac{u ^{3}}{3}]_{7}^{23}

Compute the boundaries:

\frac{23 23 - 7 7}{3}

= \frac{23 23 - 7 7}{3}

\int_{\frac{1}{2}}^{1} x^{2} ln (x) d x

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

\int_{0}^{1} 7 cos (\frac{π x}{2}) d x

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

\int_{0}^{\frac{3 π}{4}} sec^{2} (θ) d θ

What is the integral from 0 to 4 of xsqrt(x^2+7) ?
The integral from 0 to 4 of xsqrt(x^2+7) is (23sqrt(23)-7sqrt(7))/3