What is the integral of ((x^3+2x-7)/x) ?

The integral of ((x^3+2x-7)/x) is (x^3)/3+2x-7ln|x|+C

Popular >

integral of ((x^3+2x-7)/x)

\int (\frac{x ^{3} + 2 x - 7}{x}) d x

\frac{x ^{3}}{3} + 2 x - 7 ln ∣ x ∣ + C

Solution steps

\int \frac{x ^{3} + 2 x - 7}{x} d x

Expand

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

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

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

\int 2 d x = 2 x

\int \frac{7}{x} d x = 7 ln ∣ x ∣

= \frac{x ^{3}}{3} + 2 x - 7 ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{3}}{3} + 2 x - 7 ln ∣ x ∣ + C

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

\int \frac{( 2 - x ^{2} )}{x ^{4}} d x

\int \frac{x + 4}{x ^{2} + 4 x + 6} d x

\int (π) d x

\int \frac{1}{x \cdot sin ^{2} ( ln ( x ) )} d x

What is the integral of ((x^3+2x-7)/x) ?
The integral of ((x^3+2x-7)/x) is (x^3)/3+2x-7ln|x|+C