What is the integral of ((((x)+1)*(x-1)))/((x)) ?

The integral of ((((x)+1)*(x-1)))/((x)) is (x^2)/2-ln|x|+C

Popular >

integral of ((((x)+1)*(x-1)))/((x))

\int \frac{( ( ( x ) + 1 ) \cdot ( x - 1 ) )}{( x )} d x

\frac{x ^{2}}{2} - ln ∣ x ∣ + C

Solution steps

\int \frac{( x + 1 ) ( x - 1 )}{x} d x

Expand

\frac{( x + 1 ) ( x - 1 )}{x} : x - \frac{1}{x}

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

= \frac{x ^{2}}{2} - ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{2}}{2} - ln ∣ x ∣ + C

f (x) = x^{2} + 2, (- 2, 6)

\int 2^{x - 1} d x

(2) (e^{3 x x})

\int (x + 1) e^{8 x^{2} + 16 x} d x

\frac{\partial}{\partial x} (\frac{1}{2 x + y})

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