What is the integral from 4 to 11 of x/(sqrt(x+5)) ?

The integral from 4 to 11 of x/(sqrt(x+5)) is 44/3

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integral from 4 to 11 of x/(sqrt(x+5))

\int_{4}^{11} \frac{x}{x + 5} d x

\frac{44}{3}

Decimal Notation

14.66666 \dots

Solution steps

\int_{4}^{11} \frac{x}{x + 5} d x

Apply u-substitution

: \int_{3}^{4} 2 (u^{2} - 5) d u

= \int_{3}^{4} 2 (u^{2} - 5) d u

Take the constant out:

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

= 2 \cdot \int_{3}^{4} u^{2} - 5 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

= 2 (\int_{3}^{4} u^{2} d u - \int_{3}^{4} 5 d u)

\int_{3}^{4} u^{2} d u = \frac{37}{3}

\int_{3}^{4} 5 d u = 5

= 2 (\frac{37}{3} - 5)

Simplify

2 (\frac{37}{3} - 5) : \frac{44}{3}

= \frac{44}{3}

\int_{1}^{e} 1 - ln (y) d y

\int_{0}^{5} (x + 3) d x

\int_{3}^{5} - 5 t d t

\int_{0}^{1} \frac{x e ^{- 2 x}}{2} d x

\int_{- 1}^{1} \frac{x + 2}{x} d x

What is the integral from 4 to 11 of x/(sqrt(x+5)) ?
The integral from 4 to 11 of x/(sqrt(x+5)) is 44/3