What is the integral from 2 to 6 of 2/x-4/(x^2) ?

The integral from 2 to 6 of 2/x-4/(x^2) is 2ln(3)-4/3

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integral from 2 to 6 of 2/x-4/(x^2)

\int_{2}^{6} \frac{2}{x} - \frac{4}{x ^{2}} d x

2 ln (3) - \frac{4}{3}

Decimal

0.86389 \dots

Solution steps

\int_{2}^{6} \frac{2}{x} - \frac{4}{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}^{6} \frac{2}{x} d x - \int_{2}^{6} \frac{4}{x ^{2}} d x

\int_{2}^{6} \frac{2}{x} d x = 2 ln (3)

\int_{2}^{6} \frac{4}{x ^{2}} d x = \frac{4}{3}

= 2 ln (3) - \frac{4}{3}

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What is the integral from 2 to 6 of 2/x-4/(x^2) ?
The integral from 2 to 6 of 2/x-4/(x^2) is 2ln(3)-4/3