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

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

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

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

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

Solution steps

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

9 - 9 x^{2} = 3 1 - x^{2}

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

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

Use the common integral:

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

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

Simplify

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

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

Add a constant to the solution

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

\int \frac{1}{( x ^{2} + 2 x + 5 ) ^{3}} d x

sec (tan (x))

\frac{d}{d x} (\frac{6 x ^{2} + 2 x + 2}{x})

x y^{^{'}} + 3 y = \frac{( 2 e ^{4 x} )}{x ^{2}}

\int \frac{1}{x ^{2} + 3 ^{2}} d x

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