What is the integral of (x^3+2x^2+5)/x ?

The integral of (x^3+2x^2+5)/x is (x^3)/3+x^2+5ln|x|+C

Popular >

integral of (x^3+2x^2+5)/x

\int \frac{x ^{3} + 2 x ^{2} + 5}{x} d x

\frac{x ^{3}}{3} + x^{2} + 5 ln ∣ x ∣ + C

Solution steps

\int \frac{x ^{3} + 2 x ^{2} + 5}{x} d x

Expand

\frac{x ^{3} + 2 x ^{2} + 5}{x} : x^{2} + 2 x + \frac{5}{x}

= \int x^{2} + 2 x + \frac{5}{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^{2} d x + \int 2 x d x + \int \frac{5}{x} d x

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

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

\int \frac{5}{x} d x = 5 ln ∣ x ∣

= \frac{x ^{3}}{3} + x^{2} + 5 ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{3}}{3} + x^{2} + 5 ln ∣ x ∣ + C

\int \frac{1}{m} d m

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

\int e^{- 5 t} t d t

\int - 8 tan (4 x) d x

\int \frac{sin ( x )}{cos ^{2} ( x )} x d x

What is the integral of (x^3+2x^2+5)/x ?
The integral of (x^3+2x^2+5)/x is (x^3)/3+x^2+5ln|x|+C