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

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

integral of ((2x-3))/(sqrt(9-x^2))

\int \frac{( 2 x - 3 )}{9 - x ^{2}} d x

- 2 9 - x^{2} - 3 arcsin (\frac{1}{3} x) + C

Solution steps

\int \frac{2 x - 3}{9 - x ^{2}} d x

Expand

\frac{2 x - 3}{9 - x ^{2}} : \frac{2 x}{9 - x ^{2}} - \frac{3}{9 - x ^{2}}

= \int \frac{2 x}{9 - x ^{2}} - \frac{3}{9 - x ^{2}} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{2 x}{9 - x ^{2}} d x - \int \frac{3}{9 - x ^{2}} d x

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

\int \frac{3}{9 - x ^{2}} d x = 3 arcsin (\frac{1}{3} x)

= - 2 9 - x^{2} - 3 arcsin (\frac{1}{3} x)

Add a constant to the solution

= - 2 9 - x^{2} - 3 arcsin (\frac{1}{3} x) + C

y^{^{'}} = - 0.5 y^{1.5}

\frac{\partial}{\partial y} (x arcsin (\frac{y}{x}))

f (x) = (x + 5) (9 x + 5)

\frac{d}{d x} ((cos (x) + 2)^{3} (2 x)^{(- 3 x)})

\int (e^{- x^{2}}) d x

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