What is the integral of (5/(sqrt(1-x^2))+3/x) ?

The integral of (5/(sqrt(1-x^2))+3/x) is 5arcsin(x)+3ln|x|+C

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integral of (5/(sqrt(1-x^2))+3/x)

\int (\frac{5}{1 - x ^{2}} + \frac{3}{x}) d x

5 arcsin (x) + 3 ln ∣ x ∣ + C

Solution steps

\int \frac{5}{1 - x ^{2}} + \frac{3}{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{5}{1 - x ^{2}} d x + \int \frac{3}{x} d x

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

\int \frac{3}{x} d x = 3 ln ∣ x ∣

= 5 arcsin (x) + 3 ln ∣ x ∣

Add a constant to the solution

= 5 arcsin (x) + 3 ln ∣ x ∣ + C

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What is the integral of (5/(sqrt(1-x^2))+3/x) ?
The integral of (5/(sqrt(1-x^2))+3/x) is 5arcsin(x)+3ln|x|+C