What is the integral of (2x)/(sqrt(x^2-27)) ?

The integral of (2x)/(sqrt(x^2-27)) is 2sqrt(x^2-27)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2x)/(sqrt(x^2-27))

\int \frac{2 x}{x ^{2} - 27} d x

2 x^{2} - 27 + C

Solution steps

\int \frac{2 x}{x ^{2} - 27} d x

Take the constant out:

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

= 2 \cdot \int \frac{x}{x ^{2} - 27} d x

Apply u-substitution

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

= 2 \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

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

Apply the Power Rule

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

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

Substitute back

u = x^{2} - 27

= 2 \cdot \frac{1}{2} \cdot 2 (x^{2} - 27)^{\frac{1}{2}}

Simplify

2 \cdot \frac{1}{2} \cdot 2 (x^{2} - 27)^{\frac{1}{2}} : 2 x^{2} - 27

= 2 x^{2} - 27

Add a constant to the solution

= 2 x^{2} - 27 + C

\int \frac{3}{2} x d x

y^{^{'}} = y sin (4 x)

\frac{d}{d y} (2 x sin (y))

\frac{\partial}{\partial x} (- (x - 4)^{2} - (y - 1)^{2})

\int \frac{1}{x} d x

What is the integral of (2x)/(sqrt(x^2-27)) ?
The integral of (2x)/(sqrt(x^2-27)) is 2sqrt(x^2-27)+C