What is the integral of (3x^2+2x+1)/x ?

The integral of (3x^2+2x+1)/x is (3x^2)/2+2x+ln|x|+C

integral of (3x^2+2x+1)/x

\int \frac{3 x ^{2} + 2 x + 1}{x} d x

\frac{3 x ^{2}}{2} + 2 x + ln ∣ x ∣ + C

Solution steps

\int \frac{3 x ^{2} + 2 x + 1}{x} d x

Expand

\frac{3 x ^{2} + 2 x + 1}{x} : 3 x + 2 + \frac{1}{x}

= \int 3 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 3 x d x + \int 2 d x + \int \frac{1}{x} d x

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

\int 2 d x = 2 x

\int \frac{1}{x} d x = ln ∣ x ∣

= \frac{3 x ^{2}}{2} + 2 x + ln ∣ x ∣

Add a constant to the solution

= \frac{3 x ^{2}}{2} + 2 x + ln ∣ x ∣ + C

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

\int sin^{2} (4 θ) d θ

l a pl a ce t r an s f or m f (t) = 5 cos (8 t) + 3 e^{- 4} sin (3 t)

\frac{d}{d x} ((x^{3} + 1)^{4})

\int sec (x) - cos (x) d x

What is the integral of (3x^2+2x+1)/x ?
The integral of (3x^2+2x+1)/x is (3x^2)/2+2x+ln|x|+C