What is the integral from 2 to 4 of x/(x-1) ?

The integral from 2 to 4 of x/(x-1) is 2+ln(3)

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integral from 2 to 4 of x/(x-1)

\int_{2}^{4} \frac{x}{x - 1} d x

2 + ln (3)

Decimal

3.09861 \dots

Solution steps

\int_{2}^{4} \frac{x}{x - 1} d x

Apply u-substitution

: \int_{1}^{3} \frac{u + 1}{u} d u

= \int_{1}^{3} \frac{u + 1}{u} d u

Expand

\frac{u + 1}{u} : 1 + \frac{1}{u}

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

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

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

= 2 + ln (3)

\int_{0}^{4} (x^{2} + 2) d x

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

\int_{0}^{1} 4 + 5 x d x

\int_{- 4}^{3} (- x^{2} - x + 12) d x

\int_{0}^{8} (64 - x^{2}) d x

What is the integral from 2 to 4 of x/(x-1) ?
The integral from 2 to 4 of x/(x-1) is 2+ln(3)