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 Notation

0.60947 \dots

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

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

= [\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}

\int (2 x^{3} - x^{2} + 3 x - 7) d x

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

\int \frac{1}{7 x ^{7}} d x

\frac{d}{d x} (sin (4 x) + 2 x^{\frac{3}{2}})

sin (x), x = \frac{π}{4}

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