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

The integral from 0 to 1 of (xsqrt(x^2+1)) is (2sqrt(2)-1)/3

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

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

\frac{2 2 - 1}{3}

Decimal

0.60947 \dots

Solution steps

\int_{0}^{1} x x^{2} + 1 d x

Apply u-substitution

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

Apply the Power Rule

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

Compute the boundaries:

\frac{2 2}{3} - \frac{1}{3}

= \frac{2 2}{3} - \frac{1}{3}

Simplify

= \frac{2 2 - 1}{3}

\frac{d}{d x} (\frac{120}{( 1 - x ) ^{6}})

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\int x 5 + 2 x^{2} d x

What is the integral from 0 to 1 of (xsqrt(x^2+1)) ?
The integral from 0 to 1 of (xsqrt(x^2+1)) is (2sqrt(2)-1)/3