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

The integral from 0 to 1 of (2x-2)/(x+3) is 2-8(2ln(2)-ln(3))

Popular >

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

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

2 - 8 (2 ln (2) - ln (3))

Decimal

- 0.30145 \dots

Solution steps

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

Apply u-substitution

: \int_{3}^{4} \frac{2 u - 8}{u} d u

= \int_{3}^{4} \frac{2 u - 8}{u} d u

Expand

\frac{2 u - 8}{u} : 2 - \frac{8}{u}

= \int_{3}^{4} 2 - \frac{8}{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_{3}^{4} 2 d u - \int_{3}^{4} \frac{8}{u} d u

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

\int_{3}^{4} \frac{8}{u} d u = 8 (2 ln (2) - ln (3))

= 2 - 8 (2 ln (2) - ln (3))

\int_{1}^{e^{6}} \frac{( ln ( x ) ) ^{2}}{x} d x

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

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

\int_{0.5}^{1} (2 - 2 x) d x

\int_{x^{1}}^{x^{2}} 1 d x

What is the integral from 0 to 1 of (2x-2)/(x+3) ?
The integral from 0 to 1 of (2x-2)/(x+3) is 2-8(2ln(2)-ln(3))