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

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

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

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

3 - \frac{2 2}{3}

Decimal

0.78924 \dots

Solution steps

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

Apply u-substitution

: \int_{2}^{3} u^{2} d u

= \int_{2}^{3} u^{2} d u

Apply the Power Rule

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

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

Compute the boundaries:

3 - \frac{2 2}{3}

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

2 \frac{d y}{d x} + y = 0

y = x^{m x}

\frac{\partial}{\partial x} (y^{2} + 2 e^{x^{2}} x y)

\int \frac{ln ( x ^{2} )}{2} d x

x^{3} + 8 x - 1, - 1

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