What is the integral of (5/(sqrt(1-x^2))-2/(x^2+1)) ?

The integral of (5/(sqrt(1-x^2))-2/(x^2+1)) is 5arcsin(x)-2arctan(x)+C

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integral of (5/(sqrt(1-x^2))-2/(x^2+1))

\int (\frac{5}{1 - x ^{2}} - \frac{2}{x ^{2} + 1}) d x

5 arcsin (x) - 2 arctan (x) + C

Solution steps

\int \frac{5}{1 - x ^{2}} - \frac{2}{x ^{2} + 1} 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{5}{1 - x ^{2}} d x - \int \frac{2}{x ^{2} + 1} d x

\int \frac{5}{1 - x ^{2}} d x = 5 arcsin (x)

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

= 5 arcsin (x) - 2 arctan (x)

Add a constant to the solution

= 5 arcsin (x) - 2 arctan (x) + C

What is the integral of (5/(sqrt(1-x^2))-2/(x^2+1)) ?
The integral of (5/(sqrt(1-x^2))-2/(x^2+1)) is 5arcsin(x)-2arctan(x)+C