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

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

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

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

1 - ln (3) + ln (2)

Decimal

0.59453 \dots

Solution steps

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

Apply u-substitution

: \int_{2}^{3} \frac{u - 1}{u} d u

= \int_{2}^{3} \frac{u - 1}{u} d u

Expand

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

= \int_{2}^{3} 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_{2}^{3} 1 d u - \int_{2}^{3} \frac{1}{u} d u

\int_{2}^{3} 1 d u = 1

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

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

Simplify

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

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