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

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

Popular >

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

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

- \frac{1}{x} + \frac{3}{2 x ^{2}} + C

Solution steps

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

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

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

= - \frac{1}{x} - (- \frac{3}{2 x ^{2}})

Simplify

= - \frac{1}{x} + \frac{3}{2 x ^{2}}

Add a constant to the solution

= - \frac{1}{x} + \frac{3}{2 x ^{2}} + C

\int e^{- 0.03 x} d x

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

\int x (10 x + 10)^{100} d x

\int \frac{4 x + 2}{x ^{2} + x + 1} d x

\int \frac{( 4 x ^{3} + 2 x ^{2} + 1 )}{4 x ^{3} - x} d x

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