What is the integral of (7/(x^2+1)-8/x) ?

The integral of (7/(x^2+1)-8/x) is 7arctan(x)-8ln|x|+C

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integral of (7/(x^2+1)-8/x)

\int (\frac{7}{x ^{2} + 1} - \frac{8}{x}) d x

7 arctan (x) - 8 ln ∣ x ∣ + C

Solution steps

\int \frac{7}{x ^{2} + 1} - \frac{8}{x} 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 \frac{7}{x ^{2} + 1} d x - \int \frac{8}{x} d x

\int \frac{7}{x ^{2} + 1} d x = 7 arctan (x)

\int \frac{8}{x} d x = 8 ln ∣ x ∣

= 7 arctan (x) - 8 ln ∣ x ∣

Add a constant to the solution

= 7 arctan (x) - 8 ln ∣ x ∣ + C

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What is the integral of (7/(x^2+1)-8/x) ?
The integral of (7/(x^2+1)-8/x) is 7arctan(x)-8ln|x|+C