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

The integral of ((1-x^3))/((1-x)) is (x^3)/3+(x^2)/2+x+C

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integral of ((1-x^3))/((1-x))

integral

\frac{( 1 - x ^{3} )}{( 1 - x )}

\frac{x ^{3}}{3} + \frac{x ^{2}}{2} + x + C

Solution steps

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

Simplify

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

= \int x^{2} + x + 1 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 x^{2} d x + \int x d x + \int 1 d x

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

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

\int 1 d x = x

= \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + x

Add a constant to the solution

= \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + x + C

\frac{1}{( 1 + lo g _{10} ( x ) )}

t^{- 1}

- e^{y} - 2

\frac{1}{( t ^{2} - 10 t + 1 )}

\frac{1}{a ^{2} + x ^{2}}

What is the integral of ((1-x^3))/((1-x)) ?
The integral of ((1-x^3))/((1-x)) is (x^3)/3+(x^2)/2+x+C