What is the integral from 1 to 4 of 5/x-5/(x^2) ?

The integral from 1 to 4 of 5/x-5/(x^2) is 10ln(2)-15/4

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integral from 1 to 4 of 5/x-5/(x^2)

\int_{1}^{4} \frac{5}{x} - \frac{5}{x ^{2}} d x

10 ln (2) - \frac{15}{4}

Decimal

3.18147 \dots

Solution steps

\int_{1}^{4} \frac{5}{x} - \frac{5}{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_{1}^{4} \frac{5}{x} d x - \int_{1}^{4} \frac{5}{x ^{2}} d x

\int_{1}^{4} \frac{5}{x} d x = 10 ln (2)

\int_{1}^{4} \frac{5}{x ^{2}} d x = \frac{15}{4}

= 10 ln (2) - \frac{15}{4}

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What is the integral from 1 to 4 of 5/x-5/(x^2) ?
The integral from 1 to 4 of 5/x-5/(x^2) is 10ln(2)-15/4