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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

Add a constant to the solution

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

y = e^{x}, y = e^{2 x}, x = 0, x = ln (4)

\frac{\partial}{\partial y} (y^{x} - ln (x^{3} y + 6 x))

x \to - 4 + lim (\frac{- 6 x}{x + 4})

\frac{\partial}{\partial x} (arctan (\frac{1}{x}))

\int e^{- s t} t sin (t) d t

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