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)))

integral

\frac{x}{( x ^{2} + 1 )}

x^{2} + 1 + C

Solution steps

\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

x^{2} (sin (x))^{2}

\frac{y - 2}{x}

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

\frac{1}{( 1 + x ^{2} )}

\frac{x ( 1 + 3 x ^{2} ) ^{5}}{2}

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