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

The integral from 0 to 1 of xsqrt(3x^2+2) is (5sqrt(5)-2sqrt(2))/9

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integral from 0 to 1 of xsqrt(3x^2+2)

\int_{0}^{1} x 3 x^{2} + 2 d x

\frac{5 5 - 2 2}{9}

Decimal

0.92799 \dots

Solution steps

\int_{0}^{1} x 3 x^{2} + 2 d x

Apply u-substitution

: \int_{2}^{5} \frac{u}{6} d u

= \int_{2}^{5} \frac{u}{6} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{6} \cdot \int_{2}^{5} u d u

Apply the Power Rule

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

= \frac{1}{6} [\frac{2}{3} u^{\frac{3}{2}}]_{2}^{5}

Compute the boundaries:

\frac{10 5 - 4 2}{3}

= \frac{1}{6} \cdot \frac{10 5 - 4 2}{3}

Simplify

= \frac{5 5 - 2 2}{9}

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What is the integral from 0 to 1 of xsqrt(3x^2+2) ?
The integral from 0 to 1 of xsqrt(3x^2+2) is (5sqrt(5)-2sqrt(2))/9