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

The integral from 1 to 2 of xsqrt(x^2+1) is (5sqrt(5)-2sqrt(2))/3

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integral from 1 to 2 of xsqrt(x^2+1)

\int_{1}^{2} x x^{2} + 1 d x

\frac{5 5 - 2 2}{3}

Decimal

2.78397 \dots

Solution steps

\int_{1}^{2} x x^{2} + 1 d x

Apply u-substitution

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

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

Apply the Power Rule

: [\frac{u ^{3}}{3}]_{2}^{5}

= [\frac{u ^{3}}{3}]_{2}^{5}

Compute the boundaries:

\frac{5 5 - 2 2}{3}

= \frac{5 5 - 2 2}{3}

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What is the integral from 1 to 2 of xsqrt(x^2+1) ?
The integral from 1 to 2 of xsqrt(x^2+1) is (5sqrt(5)-2sqrt(2))/3