What is the integral of-2/(sqrt(1-9x^2)) ?

The integral of-2/(sqrt(1-9x^2)) is -2/3 arcsin(3x)+C

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integral of-2/(sqrt(1-9x^2))

\int - \frac{2}{1 - 9 x ^{2}} d x

- \frac{2}{3} arcsin (3 x) + C

Solution steps

\int - \frac{2}{1 - 9 x ^{2}} d x

Take the constant out:

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

= - 2 \cdot \int \frac{1}{1 - 9 x ^{2}} d x

Apply Trigonometric Substitution

: \int \frac{1}{3} d u

= - 2 \cdot \int \frac{1}{3} d u

Take the constant out:

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

= - 2 \cdot \frac{1}{3} \cdot \int 1 d u

Integral of a constant:

\int a d x = a x

= - 2 \cdot \frac{1}{3} \cdot 1 \cdot u

Substitute back

u = arcsin (3 x)

= - 2 \cdot \frac{1}{3} \cdot 1 \cdot arcsin (3 x)

Simplify

- 2 \cdot \frac{1}{3} \cdot 1 \cdot arcsin (3 x) : - \frac{2}{3} arcsin (3 x)

= - \frac{2}{3} arcsin (3 x)

Add a constant to the solution

= - \frac{2}{3} arcsin (3 x) + C

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What is the integral of-2/(sqrt(1-9x^2)) ?
The integral of-2/(sqrt(1-9x^2)) is -2/3 arcsin(3x)+C