What is the integral from 0 to 1 of xsqrt(4x^2+5) ?

The integral from 0 to 1 of xsqrt(4x^2+5) is (27-5sqrt(5))/(12)

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integral from 0 to 1 of xsqrt(4x^2+5)

\int_{0}^{1} x 4 x^{2} + 5 d x

\frac{27 - 5 5}{12}

Decimal Notation

1.31830 \dots

Solution steps

\int_{0}^{1} x 4 x^{2} + 5 d x

Apply u-substitution

: \int_{5}^{9} \frac{u}{8} d u

= \int_{5}^{9} \frac{u}{8} d u

Take the constant out:

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

= \frac{1}{8} \cdot \int_{5}^{9} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{9}

= \frac{1}{8} [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{9}

Compute the boundaries:

18 - \frac{10 5}{3}

= \frac{1}{8} (18 - \frac{10 5}{3})

Simplify

= \frac{27 - 5 5}{12}

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What is the integral from 0 to 1 of xsqrt(4x^2+5) ?
The integral from 0 to 1 of xsqrt(4x^2+5) is (27-5sqrt(5))/(12)