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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

- x^{2} + 1 + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply u-substitution

: \int \frac{1}{2 u} d u

= - \int \frac{1}{2 u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \frac{1}{2} \cdot \int \frac{1}{u} d u

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= - \frac{1}{2} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = x^{2} + 1

= - \frac{1}{2} \cdot 2 (x^{2} + 1)^{\frac{1}{2}}

Simplify

- \frac{1}{2} \cdot 2 (x^{2} + 1)^{\frac{1}{2}} : - x^{2} + 1

= - x^{2} + 1

Add a constant to the solution

= - x^{2} + 1 + C

\int 2 + sec^{2} (x) d x

\int 7 - x^{2} d x

\int 3 x^{2} - 4 x + 2 - e^{- x} d x

\int (1 + \frac{1}{sin ^{2} ( x )}) cos (x) d x

\int \frac{50}{x ^{2}} d x

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