What is the integral from 0 to 24/25 of sqrt(1+5x) ?

The integral from 0 to 24/25 of sqrt(1+5x) is (58sqrt(29)-10sqrt(5))/(75sqrt(5))

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integral from 0 to 24/25 of sqrt(1+5x)

\int_{0}^{\frac{24}{25}} 1 + 5 x d x

\frac{58 29 - 10 5}{75 5}

Decimal

1.72909 \dots

Solution steps

\int_{0}^{\frac{24}{25}} 1 + 5 x d x

Apply u-substitution

= \int_{1}^{\frac{29}{5}} \frac{u}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int_{1}^{\frac{29}{5}} u d u

Apply the Power Rule

= \frac{1}{5} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{\frac{29}{5}}

Compute the boundaries:

\frac{58 29}{15 5} - \frac{2}{3}

= \frac{1}{5} (\frac{58 29}{15 5} - \frac{2}{3})

Simplify

= \frac{58 29 - 10 5}{75 5}

What is the integral from 0 to 24/25 of sqrt(1+5x) ?
The integral from 0 to 24/25 of sqrt(1+5x) is (58sqrt(29)-10sqrt(5))/(75sqrt(5))