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

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

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integral of (e^2)/x-1/(sqrt(1-x^2))

\int \frac{e ^{2}}{x} - \frac{1}{1 - x ^{2}} d x

e^{2} ln ∣ x ∣ - arcsin (x) + C

Solution steps

\int \frac{e ^{2}}{x} - \frac{1}{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{e ^{2}}{x} d x - \int \frac{1}{1 - x ^{2}} d x

\int \frac{e ^{2}}{x} d x = e^{2} ln ∣ x ∣

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

= e^{2} ln ∣ x ∣ - arcsin (x)

Add a constant to the solution

= e^{2} ln ∣ x ∣ - arcsin (x) + C

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