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

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

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

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

1 - 2 ln (2) + ln (3)

Decimal

0.71231 \dots

Solution steps

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

Apply u-substitution

: \int_{3}^{4} \frac{u - 1}{u} d u

= \int_{3}^{4} \frac{u - 1}{u} d u

Expand

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

= \int_{3}^{4} 1 - \frac{1}{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} 1 d u - \int_{3}^{4} \frac{1}{u} d u

\int_{3}^{4} 1 d u = 1

\int_{3}^{4} \frac{1}{u} d u = 2 ln (2) - ln (3)

= 1 - (2 ln (2) - ln (3))

Simplify

= 1 - 2 ln (2) + ln (3)

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