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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\int 1 - \frac{x}{y - x ^{2}}

x + y - x^{2} + C

Solution steps

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

\int 1 d x = x

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

= x - (- y - x^{2})

Simplify

= x + y - x^{2}

Add a constant to the solution

= x + y - x^{2} + C

\frac{d y}{d x} = \frac{1}{10} \cdot y \cdot (500 - y)

\frac{d}{d x} (sin^{2} (x + 5))

\frac{d}{d x} ((e^{3})^{x - 1})

\frac{d}{d x} (5 x^{8})

\int \frac{( 1 - t cos ( t ) )}{t} d t

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