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

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

Popular >

integral of (2-3x^2)/(x^3)

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

- \frac{1}{x ^{2}} - 3 ln ∣ x ∣ + C

Solution steps

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

Expand

\frac{2 - 3 x ^{2}}{x ^{3}} : \frac{2}{x ^{3}} - \frac{3}{x}

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

\int \frac{2}{x ^{3}} d x = - \frac{1}{x ^{2}}

\int \frac{3}{x} d x = 3 ln ∣ x ∣

= - \frac{1}{x ^{2}} - 3 ln ∣ x ∣

Add a constant to the solution

= - \frac{1}{x ^{2}} - 3 ln ∣ x ∣ + C

\int 1 0^{5 x} d x

\int (- 2 x^{2} + 6 x) d x

\int e^{x l n (a)} d x

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

\int cos^{7} (θ) sin (2 θ) d θ

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