What is the integral of (13)/(sqrt(36-36x^2)) ?

The integral of (13)/(sqrt(36-36x^2)) is 13/6 arcsin(x)+C

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integral of (13)/(sqrt(36-36x^2))

\int \frac{13}{36 - 36 x ^{2}} d x

\frac{13}{6} arcsin (x) + C

Solution steps

\int \frac{13}{36 - 36 x ^{2}} d x

Take the constant out:

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

= 13 \cdot \int \frac{1}{36 - 36 x ^{2}} d x

36 - 36 x^{2} = 6 1 - x^{2}

= 13 \cdot \int \frac{1}{6 1 - x ^{2}} d x

Take the constant out:

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

= 13 \cdot \frac{1}{6} \cdot \int \frac{1}{1 - x ^{2}} d x

Use the common integral:

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

= 13 \cdot \frac{1}{6} arcsin (x)

Simplify

13 \cdot \frac{1}{6} arcsin (x) : \frac{13}{6} arcsin (x)

= \frac{13}{6} arcsin (x)

Add a constant to the solution

= \frac{13}{6} arcsin (x) + C

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What is the integral of (13)/(sqrt(36-36x^2)) ?
The integral of (13)/(sqrt(36-36x^2)) is 13/6 arcsin(x)+C