What is the integral from 0 to 2 of 4/(sqrt(5x+3)) ?

The integral from 0 to 2 of 4/(sqrt(5x+3)) is (4(2sqrt(13)-2sqrt(3)))/5

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integral from 0 to 2 of 4/(sqrt(5x+3))

\int_{0}^{2} \frac{4}{5 x + 3} d x

\frac{4 ( 2 13 - 2 3 )}{5}

Decimal

2.99760 \dots

Solution steps

\int_{0}^{2} \frac{4}{5 x + 3} d x

Take the constant out:

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

= 4 \cdot \int_{0}^{2} \frac{1}{5 x + 3} d x

Apply u-substitution

: \int_{3}^{13} \frac{1}{5 u} d u

= 4 \cdot \int_{3}^{13} \frac{1}{5 u} d u

Take the constant out:

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

= 4 \cdot \frac{1}{5} \cdot \int_{3}^{13} \frac{1}{u} d u

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{3}^{13}

= 4 \cdot \frac{1}{5} [2 u^{\frac{1}{2}}]_{3}^{13}

Simplify

4 \cdot \frac{1}{5} [2 u^{\frac{1}{2}}]_{3}^{13} : \frac{4}{5} [2 u]_{3}^{13}

= \frac{4}{5} [2 u]_{3}^{13}

Compute the boundaries:

213 - 23

= \frac{4}{5} (213 - 23)

Simplify

= \frac{4 ( 2 13 - 2 3 )}{5}

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What is the integral from 0 to 2 of 4/(sqrt(5x+3)) ?
The integral from 0 to 2 of 4/(sqrt(5x+3)) is (4(2sqrt(13)-2sqrt(3)))/5