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

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

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integral of (x^3-1)/x

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

\frac{x ^{3}}{3} - ln ∣ x ∣ + C

Solution steps

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

Expand

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

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

= \frac{x ^{3}}{3} - ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{3}}{3} - ln ∣ x ∣ + C

\frac{d y}{d x} = 21 x^{2} e^{- y}

x + y = 2, x = y^{2} - 2 y

\frac{d}{d x} (\frac{( x ^{2} - 5 ) ^{3}}{125})

x \to \infty lim (\frac{k}{x})

\int (x)^{\frac{3}{2}} d x

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