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

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

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

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

\frac{x ^{4}}{4 a} + \frac{a}{2 x ^{2}} + C

Solution steps

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

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

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

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

Simplify

= \frac{x ^{4}}{4 a} + \frac{a}{2 x ^{2}}

Add a constant to the solution

= \frac{x ^{4}}{4 a} + \frac{a}{2 x ^{2}} + C

\frac{d}{d x} (x^{22})

2 x y + (2 y + x^{2}) \cdot (\frac{d y}{d x}) = 0

\frac{d}{d x} (- e^{x^{2} - 5 x})

\int \frac{1}{( X ^{2} + 1 ) ^{2}} d X

x \to + 0 - lim (\frac{2}{x})

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