What is the integral from 0 to 3 of 1/(sqrt(3x+5)) ?

The integral from 0 to 3 of 1/(sqrt(3x+5)) is (2sqrt(14)-2sqrt(5))/3

Popular >

integral from 0 to 3 of 1/(sqrt(3x+5))

\int_{0}^{3} \frac{1}{3 x + 5} d x

\frac{2 14 - 2 5}{3}

Decimal

1.00372 \dots

Solution steps

\int_{0}^{3} \frac{1}{3 x + 5} d x

Apply u-substitution

: \int_{5}^{14} \frac{1}{3 u} d u

= \int_{5}^{14} \frac{1}{3 u} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int_{5}^{14} \frac{1}{u} d u

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{5}^{14}

= \frac{1}{3} [2 u^{\frac{1}{2}}]_{5}^{14}

Apply radical rule:

a^{\frac{1}{n}} = n a

= \frac{1}{3} [2 u]_{5}^{14}

Compute the boundaries:

214 - 25

= \frac{1}{3} (214 - 25)

Simplify

= \frac{2 14 - 2 5}{3}

\int_{0}^{4} (y - 3) (2 y + 2) d y

\int_{0}^{5} 255 - (9 x^{2} + 2 x + 20) d x

\int_{0}^{1} e^{t} + e^{- t} d t

\int_{3}^{4} (- x^{2} + 17) d x

\int_{1}^{8} \frac{3}{t} d t

What is the integral from 0 to 3 of 1/(sqrt(3x+5)) ?
The integral from 0 to 3 of 1/(sqrt(3x+5)) is (2sqrt(14)-2sqrt(5))/3