What is the integral of 3/(1+x^2)-2/(sqrt(1-x^2)) ?

The integral of 3/(1+x^2)-2/(sqrt(1-x^2)) is 3arctan(x)-2arcsin(x)+C

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integral of 3/(1+x^2)-2/(sqrt(1-x^2))

\int \frac{3}{1 + x ^{2}} - \frac{2}{1 - x ^{2}} d x

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

Solution steps

\int \frac{3}{1 + x ^{2}} - \frac{2}{1 - 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 \frac{3}{1 + x ^{2}} d x - \int \frac{2}{1 - x ^{2}} d x

\int \frac{3}{1 + x ^{2}} d x = 3 arctan (x)

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

= 3 arctan (x) - 2 arcsin (x)

Add a constant to the solution

= 3 arctan (x) - 2 arcsin (x) + C

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What is the integral of 3/(1+x^2)-2/(sqrt(1-x^2)) ?
The integral of 3/(1+x^2)-2/(sqrt(1-x^2)) is 3arctan(x)-2arcsin(x)+C