What is the integral of (4/(x^2+1)-7/x) ?

The integral of (4/(x^2+1)-7/x) is 4arctan(x)-7ln|x|+C

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integral of (4/(x^2+1)-7/x)

\int (\frac{4}{x ^{2} + 1} - \frac{7}{x}) d x

4 arctan (x) - 7 ln ∣ x ∣ + C

Solution steps

\int \frac{4}{x ^{2} + 1} - \frac{7}{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{4}{x ^{2} + 1} d x - \int \frac{7}{x} d x

\int \frac{4}{x ^{2} + 1} d x = 4 arctan (x)

\int \frac{7}{x} d x = 7 ln ∣ x ∣

= 4 arctan (x) - 7 ln ∣ x ∣

Add a constant to the solution

= 4 arctan (x) - 7 ln ∣ x ∣ + C

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What is the integral of (4/(x^2+1)-7/x) ?
The integral of (4/(x^2+1)-7/x) is 4arctan(x)-7ln|x|+C