What is the integral of 1/(sqrt(1-\frac{x^2){81)}} ?

The integral of 1/(sqrt(1-\frac{x^2){81)}} is 9arcsin(1/9 x)+C

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integral of 1/(sqrt(1-\frac{x^2){81)}}

\int \frac{1}{1 - \frac{x ^{2}}{81}} d x

9 arcsin (\frac{1}{9} x) + C

Solution steps

\int \frac{1}{1 - \frac{x ^{2}}{81}} d x

Apply Trigonometric Substitution

: \int 9 d u

= \int 9 d u

Take the constant out:

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

= 9 \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= 9 \cdot 1 \cdot u

Substitute back

u = arcsin (\frac{1}{9} x)

= 9 \cdot 1 \cdot arcsin (\frac{1}{9} x)

Simplify

= 9 arcsin (\frac{1}{9} x)

Add a constant to the solution

= 9 arcsin (\frac{1}{9} x) + C

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What is the integral of 1/(sqrt(1-\frac{x^2){81)}} ?
The integral of 1/(sqrt(1-\frac{x^2){81)}} is 9arcsin(1/9 x)+C