What is the integral of (4x)/(sqrt(x^2+1)) ?

The integral of (4x)/(sqrt(x^2+1)) is 4sqrt(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 (4x)/(sqrt(x^2+1))

\int \frac{4 x}{x ^{2} + 1} d x

4 x^{2} + 1 + C

Solution steps

\int \frac{4 x}{x ^{2} + 1} d x

Take the constant out:

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

= 4 \cdot \int \frac{x}{x ^{2} + 1} d x

Apply u-substitution

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

= 4 \cdot \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

= 4 \cdot \frac{1}{2} \cdot \int \frac{1}{u} d u

Apply the Power Rule

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

= 4 \cdot \frac{1}{2} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = x^{2} + 1

= 4 \cdot \frac{1}{2} \cdot 2 (x^{2} + 1)^{\frac{1}{2}}

Simplify

4 \cdot \frac{1}{2} \cdot 2 (x^{2} + 1)^{\frac{1}{2}} : 4 x^{2} + 1

= 4 x^{2} + 1

Add a constant to the solution

= 4 x^{2} + 1 + C

\int x^{2} \cdot 2^{x} d x

f (x) = x + x^{\frac{2}{3}} - 3 x

x \to 0 lim (2 sin (x) ln (x))

2 e^{x} - e^{x + 1} + e^{\frac{2}{3}} - 5 π^{2}

x \to 0 + lim (sin^{2} (x))

What is the integral of (4x)/(sqrt(x^2+1)) ?
The integral of (4x)/(sqrt(x^2+1)) is 4sqrt(x^2+1)+C