What is the integral from 5 to 9 of x/(x+4) ?

The integral from 5 to 9 of x/(x+4) is 4-4(ln(13)-2ln(3))

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integral from 5 to 9 of x/(x+4)

\int_{5}^{9} \frac{x}{x + 4} d x

4 - 4 (ln (13) - 2 ln (3))

Decimal

2.52910 \dots

Solution steps

\int_{5}^{9} \frac{x}{x + 4} d x

Apply u-substitution

: \int_{9}^{13} \frac{u - 4}{u} d u

= \int_{9}^{13} \frac{u - 4}{u} d u

Expand

\frac{u - 4}{u} : 1 - \frac{4}{u}

= \int_{9}^{13} 1 - \frac{4}{u} 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

= \int_{9}^{13} 1 d u - \int_{9}^{13} \frac{4}{u} d u

\int_{9}^{13} 1 d u = 4

\int_{9}^{13} \frac{4}{u} d u = 4 (ln (13) - 2 ln (3))

= 4 - 4 (ln (13) - 2 ln (3))

\int_{0}^{1.4} \frac{2 x}{9} d x

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

\int_{- 1}^{1} \frac{x + 3}{x ^{2} + 2 x + 5} d x

\int_{0}^{1} \frac{x}{x ^{2} - 3 x} d x

\int_{0}^{t} e^{- u} (t - u)^{2} d u

What is the integral from 5 to 9 of x/(x+4) ?
The integral from 5 to 9 of x/(x+4) is 4-4(ln(13)-2ln(3))