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

The integral of (x^3-x)/(x^3) is x+1/x+C

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

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

x + \frac{1}{x} + C

Solution steps

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

Simplify

\frac{x ^{3} - x}{x ^{3}} : \frac{x ^{2} - 1}{x ^{2}}

= \int \frac{x ^{2} - 1}{x ^{2}} d x

Expand

\frac{x ^{2} - 1}{x ^{2}} : 1 - \frac{1}{x ^{2}}

= \int 1 - \frac{1}{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 1 d x - \int \frac{1}{x ^{2}} d x

\int 1 d x = x

\int \frac{1}{x ^{2}} d x = - \frac{1}{x}

= x - (- \frac{1}{x})

Simplify

= x + \frac{1}{x}

Add a constant to the solution

= x + \frac{1}{x} + C

n = 0 \sum \infty (- 1 + \frac{1}{e})^{n}

\frac{d}{d θ} (3 sin (3 θ))

m \frac{7}{x}

f (x) = 2 + 7 x

\frac{8}{( s + 1 ) ^{2}}

What is the integral of (x^3-x)/(x^3) ?
The integral of (x^3-x)/(x^3) is x+1/x+C