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

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

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

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

5 arcsin (y) + C

Solution steps

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

Take the constant out:

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

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

Use the common integral:

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

= 5 arcsin (y)

Add a constant to the solution

= 5 arcsin (y) + C

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