What is the integral of 1/(2x^3)-1/(x^4) ?

The integral of 1/(2x^3)-1/(x^4) is -1/(4x^2)+1/(3x^3)+C

Popular >

integral of 1/(2x^3)-1/(x^4)

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

- \frac{1}{4 x ^{2}} + \frac{1}{3 x ^{3}} + C

Solution steps

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

\int \frac{1}{2 x ^{3}} d x = - \frac{1}{4 x ^{2}}

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

= - \frac{1}{4 x ^{2}} - (- \frac{1}{3 x ^{3}})

Simplify

= - \frac{1}{4 x ^{2}} + \frac{1}{3 x ^{3}}

Add a constant to the solution

= - \frac{1}{4 x ^{2}} + \frac{1}{3 x ^{3}} + C

\frac{d}{d x} (\frac{sec ( x )}{8 + sec ( x )})

f (x) = - csc (x) cot (x)

sin (x^{0.5})

(x^{2} + 1) (2 x + 5 + \frac{8}{x})

y = \frac{x ^{2} - 4 x}{x + 1}

What is the integral of 1/(2x^3)-1/(x^4) ?
The integral of 1/(2x^3)-1/(x^4) is -1/(4x^2)+1/(3x^3)+C