What is the integral from 3 to 5 of (x+1)/(x^2-2x) ?

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

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integral from 3 to 5 of (x+1)/(x^2-2x)

\int_{3}^{5} \frac{x + 1}{x ^{2} - 2 x} d x

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

Decimal

1.39250 \dots

Solution steps

\int_{3}^{5} \frac{x + 1}{x ^{2} - 2 x} d x

Expand

\frac{x + 1}{x ^{2} - 2 x} : \frac{x}{x ^{2} - 2 x} + \frac{1}{x ^{2} - 2 x}

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}^{5} \frac{x}{x ^{2} - 2 x} d x + \int_{3}^{5} \frac{1}{x ^{2} - 2 x} d x

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

\int_{3}^{5} \frac{1}{x ^{2} - 2 x} d x = - \frac{ln ( 5 ) - 2 ln ( 3 )}{2}

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

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