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

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

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

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

\frac{1}{5}

Decimal Notation

0.2

Solution steps

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

Apply u-substitution

: \int_{4}^{9} \frac{1}{10 u} d u

= \int_{4}^{9} \frac{1}{10 u} d u

Take the constant out:

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

= \frac{1}{10} \cdot \int_{4}^{9} \frac{1}{u} d u

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{4}^{9}

= \frac{1}{10} [2 u^{\frac{1}{2}}]_{4}^{9}

Apply radical rule:

= \frac{1}{10} [2 u]_{4}^{9}

Compute the boundaries:

2

= \frac{1}{10} \cdot 2

Simplify

= \frac{1}{5}

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