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

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

Popular >

integral of ((x^2+2x+1))/x

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

\frac{x ^{2}}{2} + 2 x + ln ∣ x ∣ + C

Solution steps

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

Expand

\frac{x ^{2} + 2 x + 1}{x} : x + 2 + \frac{1}{x}

= \int x + 2 + \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 2 d x + \int \frac{1}{x} d x

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

\int 2 d x = 2 x

\int \frac{1}{x} d x = ln ∣ x ∣

= \frac{x ^{2}}{2} + 2 x + ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{2}}{2} + 2 x + ln ∣ x ∣ + C

\int \frac{e ^{2 x}}{9 + e ^{4 x}} d x

\int \frac{1}{x \cdot ( x ^{2} - 1 ) ^{\frac{1}{2}}} d x

\frac{d}{d x} (3 x^{3} - \frac{1}{x ^{3}})

e^{- 4 t} \cdot cos (3 t)

\frac{d}{d x} ((x + 1)^{3})

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