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

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

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integral of 2/(sqrt(1-t^2))

\int \frac{2}{1 - t ^{2}} d t

2 arcsin (t) + C

Solution steps

\int \frac{2}{1 - t ^{2}} d t

Take the constant out:

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

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

Use the common integral:

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

= 2 arcsin (t)

Add a constant to the solution

= 2 arcsin (t) + C

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