What is the integral of 1/(sqrt(\frac{1-x^2){100)}} ?

The integral of 1/(sqrt(\frac{1-x^2){100)}} is 10arcsin(x)+C

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integral of 1/(sqrt(\frac{1-x^2){100)}}

\int \frac{1}{\frac{1 - x ^{2}}{100}} d x

10 arcsin (x) + C

Solution steps

\int \frac{1}{\frac{1 - x ^{2}}{100}} d x

Simplify

\frac{1}{\frac{1 - x ^{2}}{100}} : \frac{10}{1 - x ^{2}}

= \int \frac{10}{1 - x ^{2}} d x

Take the constant out:

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

= 10 \cdot \int \frac{1}{1 - x ^{2}} d x

Use the common integral:

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

= 10 arcsin (x)

Add a constant to the solution

= 10 arcsin (x) + C

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What is the integral of 1/(sqrt(\frac{1-x^2){100)}} ?
The integral of 1/(sqrt(\frac{1-x^2){100)}} is 10arcsin(x)+C