What is the integral of (x^3-7)/x ?

The integral of (x^3-7)/x is (x^3)/3-7ln|x|+C

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integral of (x^3-7)/x

\int \frac{x ^{3} - 7}{x} d x

\frac{x ^{3}}{3} - 7 ln ∣ x ∣ + C

Solution steps

\int \frac{x ^{3} - 7}{x} d x

Expand

\frac{x ^{3} - 7}{x} : x^{2} - \frac{7}{x}

= \int x^{2} - \frac{7}{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{7}{x} d x

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

\int \frac{7}{x} d x = 7 ln ∣ x ∣

= \frac{x ^{3}}{3} - 7 ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{3}}{3} - 7 ln ∣ x ∣ + C

\int arctan (\frac{sin ( x )}{1 + cos ( x )}) d x

(\frac{x ^{2} + 4}{x ^{2} - 4})^{4}

\frac{d y}{d x} = (y - 1)^{3}

y = \frac{4 x + 5}{x - 1}, (2, 13)

\frac{d}{d x} (a sec (x))

What is the integral of (x^3-7)/x ?
The integral of (x^3-7)/x is (x^3)/3-7ln|x|+C