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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Solution steps

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

Expand

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

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

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

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

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

Add a constant to the solution

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

\int 27 x sec^{2} (3 x) d x

\int - y ln (y) d y

\frac{1}{( e ^{x} + 1 )}

\int 2 x + 1 x d x

\int π + x d x

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