What is the integral from 0 to 2 of (2x-1)/((x+3)^2) ?

The integral from 0 to 2 of (2x-1)/((x+3)^2) is 2ln(5)-2ln(3)-14/15

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 2 of (2x-1)/((x+3)^2)

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

2 ln (5) - 2 ln (3) - \frac{14}{15}

Decimal Notation

0.08831 \dots

Solution steps

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

Expand

\frac{2 x - 1}{( x + 3 ) ^{2}} : \frac{2 x}{( x + 3 ) ^{2}} - \frac{1}{( x + 3 ) ^{2}}

Apply the Sum Rule:

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

= \int_{0}^{2} \frac{2 x}{( x + 3 ) ^{2}} d x - \int_{0}^{2} \frac{1}{( x + 3 ) ^{2}} d x

\int_{0}^{2} \frac{2 x}{( x + 3 ) ^{2}} d x = 2 (ln (5) - ln (3) - \frac{2}{5})

\int_{0}^{2} \frac{1}{( x + 3 ) ^{2}} d x = \frac{2}{15}

= 2 (ln (5) - ln (3) - \frac{2}{5}) - \frac{2}{15}

Simplify

2 (ln (5) - ln (3) - \frac{2}{5}) - \frac{2}{15} : 2 ln (5) - 2 ln (3) - \frac{14}{15}

= 2 ln (5) - 2 ln (3) - \frac{14}{15}

\int_{0.4}^{1} x (1 - x)^{8} d x

\int_{1}^{3} (3 x^{2} - x) d x

\int_{1}^{4} e^{- x} x - e^{- x} d x

\int_{- 42.25}^{0} (\frac{13}{2} x)^{2} d x

What is the integral from 0 to 2 of (2x-1)/((x+3)^2) ?
The integral from 0 to 2 of (2x-1)/((x+3)^2) is 2ln(5)-2ln(3)-14/15