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

The integral of ((x^3)/3-3/(x^3)) is (x^4)/(12)+3/(2x^2)+C

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

\int (\frac{x ^{3}}{3} - \frac{3}{x ^{3}}) d x

\frac{x ^{4}}{12} + \frac{3}{2 x ^{2}} + C

Solution steps

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

\int \frac{x ^{3}}{3} d x = \frac{x ^{4}}{12}

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

= \frac{x ^{4}}{12} - (- \frac{3}{2 x ^{2}})

Simplify

= \frac{x ^{4}}{12} + \frac{3}{2 x ^{2}}

Add a constant to the solution

= \frac{x ^{4}}{12} + \frac{3}{2 x ^{2}} + C

y = x^{3} + x^{2} + x - 1, y = x^{3} + 5

\frac{d y}{d t} = 2 y + y^{5}, y (0) = 1

\frac{- 1}{s + 1}

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

x \to 3 lim (\frac{1}{2 ^{x} - 8})

What is the integral of ((x^3)/3-3/(x^3)) ?
The integral of ((x^3)/3-3/(x^3)) is (x^4)/(12)+3/(2x^2)+C