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

The integral from-1 to 4 of (x/(sqrt(5+x))) is 8/3

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

\int_{- 1}^{4} (\frac{x}{5 + x}) d x

\frac{8}{3}

Decimal Notation

2.66666 \dots

Solution steps

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

Apply u-substitution

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

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

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

\int_{2}^{3} 5 d u = 5

= 2 (\frac{19}{3} - 5)

Simplify

2 (\frac{19}{3} - 5) : \frac{8}{3}

= \frac{8}{3}

\int (- 7 - 7 tan^{2} (x)) d x

x \frac{d y}{d x} - 3 y = y^{2}, y (1) = 3

\int \frac{- y}{x ^{2} + y ^{2}} d x

\int 5 cos (x) + 2 sin (x) d x

f (x) = 3 x^{\frac{2}{3}} - 3, at x = 27

What is the integral from-1 to 4 of (x/(sqrt(5+x))) ?
The integral from-1 to 4 of (x/(sqrt(5+x))) is 8/3