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

The integral from 2 to 5 of (3x+3)/(x^2) is 3(ln(5)-ln(2))+9/10

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

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

3 (ln (5) - ln (2)) + \frac{9}{10}

Decimal Notation

3.64887 \dots

Solution steps

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

Expand

\frac{3 x + 3}{x ^{2}} : \frac{3}{x} + \frac{3}{x ^{2}}

= \int_{2}^{5} \frac{3}{x} + \frac{3}{x ^{2}} d 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_{2}^{5} \frac{3}{x} d x + \int_{2}^{5} \frac{3}{x ^{2}} d x

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

\int_{2}^{5} \frac{3}{x ^{2}} d x = \frac{9}{10}

= 3 (ln (5) - ln (2)) + \frac{9}{10}

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\int 10 e^{5 x} d x

What is the integral from 2 to 5 of (3x+3)/(x^2) ?
The integral from 2 to 5 of (3x+3)/(x^2) is 3(ln(5)-ln(2))+9/10