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

The integral from 0 to 1 of x/(sqrt(4+5x)) is 14/75

Popular >

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

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

\frac{14}{75}

Decimal

0.18666 \dots

Solution steps

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

Apply u-substitution

: \int_{2}^{3} \frac{2 ( u ^{2} - 4 )}{25} d u

= \int_{2}^{3} \frac{2 ( u ^{2} - 4 )}{25} d u

Take the constant out:

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

= \frac{2}{25} \cdot \int_{2}^{3} u^{2} - 4 d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{2}{25} (\int_{2}^{3} u^{2} d u - \int_{2}^{3} 4 d u)

\int_{2}^{3} u^{2} d u = \frac{19}{3}

\int_{2}^{3} 4 d u = 4

= \frac{2}{25} (\frac{19}{3} - 4)

Simplify

\frac{2}{25} (\frac{19}{3} - 4) : \frac{14}{75}

= \frac{14}{75}

\int_{\frac{π}{2}}^{2 π} \frac{1}{2} x d x

\int_{0}^{3} \frac{1}{x ( 1 + x )} d x

\int_{- 1}^{1} e^{∣ x ∣} d x

\int_{0}^{6} - 2 x^{2} + 12 x d x

\int_{a}^{a^{2}} x^{2} d x

What is the integral from 0 to 1 of x/(sqrt(4+5x)) ?
The integral from 0 to 1 of x/(sqrt(4+5x)) is 14/75