What is the integral of (3-x)/(sqrt(1-x^2)) ?

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

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integral of (3-x)/(sqrt(1-x^2))

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

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

Solution steps

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

Expand

\frac{3 - x}{1 - x ^{2}} : \frac{3}{1 - x ^{2}} - \frac{x}{1 - x ^{2}}

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

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

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

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

Simplify

= 3 arcsin (x) + 1 - x^{2}

Add a constant to the solution

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

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

\frac{\partial}{\partial t} (t e^{\frac{w}{t}})

\int x (4 x + 1) d x

\frac{df}{d t} = 4 t + \frac{9 t}{9 - t ^{2}}

x \cdot y^{2}

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