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

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

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

\int \frac{( x ^{3} - 4 )}{x ^{3}} d x

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

Solution steps

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

Expand

\frac{x ^{3} - 4}{x ^{3}} : 1 - \frac{4}{x ^{3}}

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

\int 1 d x = x

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

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

Simplify

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

Add a constant to the solution

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

sin (\frac{x}{2})

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