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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\int (x + \frac{2}{x}) (x - \frac{2}{x}) d x

\frac{x ^{2}}{2} + \frac{4}{x} + C

Solution steps

\int (x + \frac{2}{x}) (x - \frac{2}{x}) d x

Multiply by the conjugate of

x + \frac{2}{x} : \frac{x - \frac{4}{x ^{2}}}{x - \frac{2}{x}}

= \int \frac{x - \frac{4}{x ^{2}}}{x - \frac{2}{x}} (x - \frac{2}{x}) d x

Simplify

\frac{x - \frac{4}{x ^{2}}}{x - \frac{2}{x}} (x - \frac{2}{x}) : x - \frac{4}{x ^{2}}

= \int x - \frac{4}{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 x d x - \int \frac{4}{x ^{2}} d x

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

\int \frac{4}{x ^{2}} d x = - \frac{4}{x}

= \frac{x ^{2}}{2} - (- \frac{4}{x})

Simplify

= \frac{x ^{2}}{2} + \frac{4}{x}

Add a constant to the solution

= \frac{x ^{2}}{2} + \frac{4}{x} + C

\int - 14 x d x

\int \frac{1}{3} e^{3 x + 1} d x

y = sin (4 x), (0.1, 0.4)

\int cos^{2} (5 θ) d θ

\frac{\partial}{\partial x} (sin (2 x))

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