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

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

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

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

sec (x) + arcsin (x) + C

Solution steps

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

\int sec (x) tan (x) d x = sec (x)

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

= sec (x) + arcsin (x)

Add a constant to the solution

= sec (x) + arcsin (x) + C

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