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

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

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

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

\frac{1}{2} arcsin (x) - 3 arctan (x) + C

Solution steps

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

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

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

= \frac{1}{2} arcsin (x) - 3 arctan (x)

Add a constant to the solution

= \frac{1}{2} arcsin (x) - 3 arctan (x) + C

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