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

\int \frac{x ^{2}}{x ^{2} + 9} d x

x \to - π - lim (csc (x))

x^{^{''}} + 2 x^{^{'}} + 2 = 0

n = 0 \sum \infty \frac{10}{3 ^{n}}

\frac{\partial}{\partial x} ((x + y)^{p} - b x - (1 - b) y)

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