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

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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

x \to - \infty lim (e^{2} x^{2})

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

\int \frac{4400 q}{4 q ^{2} + 320} d q

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

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