What is the integral from 0 to 1 of xsqrt(x^2+4) ?

The integral from 0 to 1 of xsqrt(x^2+4) is (5sqrt(5)-8)/3

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integral from 0 to 1 of xsqrt(x^2+4)

\int_{0}^{1} x x^{2} + 4 d x

\frac{5 5 - 8}{3}

Decimal

1.06011 \dots

Solution steps

\int_{0}^{1} x x^{2} + 4 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}{3} - \frac{8}{3}

= \frac{5 5}{3} - \frac{8}{3}

Simplify

= \frac{5 5 - 8}{3}

\frac{\partial}{\partial x} (x^{2})

\int x^{4} - 8 x^{3} + 26 x^{2} - 40 x + 25 d x

x \to 6 lim (2 x - 3)

x \to 7 lim (\frac{x - 7}{x - 7})

\frac{d}{d x} (x^{3} - 5 e^{2 x})

What is the integral from 0 to 1 of xsqrt(x^2+4) ?
The integral from 0 to 1 of xsqrt(x^2+4) is (5sqrt(5)-8)/3