What is the integral of (x^2+4)/(x^3) ?

The integral of (x^2+4)/(x^3) is ln|x|-2/(x^2)+C

Popular >

integral of (x^2+4)/(x^3)

\int \frac{x ^{2} + 4}{x ^{3}} d x

ln ∣ x ∣ - \frac{2}{x ^{2}} + C

Solution steps

\int \frac{x ^{2} + 4}{x ^{3}} d x

Expand

\frac{x ^{2} + 4}{x ^{3}} : \frac{1}{x} + \frac{4}{x ^{3}}

= \int \frac{1}{x} + \frac{4}{x ^{3}} 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 \frac{1}{x} d x + \int \frac{4}{x ^{3}} d x

\int \frac{1}{x} d x = ln ∣ x ∣

\int \frac{4}{x ^{3}} d x = - \frac{2}{x ^{2}}

= ln ∣ x ∣ - \frac{2}{x ^{2}}

Add a constant to the solution

= ln ∣ x ∣ - \frac{2}{x ^{2}} + C

x^{3} e^{x^{2}}

\int \frac{6 x ^{2} + 5 x + 4}{( 1 + x ) ( 1 + 4 x ^{2} )} d x

\int \frac{2 x ^{3} + 5 x}{x ^{4} + 5 x ^{2} + 4} d x

\int x^{2} y^{3} - \frac{1}{1 + 9 x ^{2}} d x

\int (csc (x) + cot (x))^{2} d x

What is the integral of (x^2+4)/(x^3) ?
The integral of (x^2+4)/(x^3) is ln|x|-2/(x^2)+C