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

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

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

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

5 arcsin (x) + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int \frac{1}{1 - x ^{2}} d x

Use the common integral:

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

= 5 arcsin (x)

Add a constant to the solution

= 5 arcsin (x) + C

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