What is the integral of (7x^2-9x+1)/x ?

The integral of (7x^2-9x+1)/x is (7x^2)/2-9x+ln|x|+C

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integral of (7x^2-9x+1)/x

integral

\frac{7 x ^{2} - 9 x + 1}{x}

\frac{7 x ^{2}}{2} - 9 x + ln ∣ x ∣ + C

Solution steps

\int \frac{7 x ^{2} - 9 x + 1}{x} d x

Expand

\frac{7 x ^{2} - 9 x + 1}{x} : 7 x - 9 + \frac{1}{x}

= \int 7 x - 9 + \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 7 x d x - \int 9 d x + \int \frac{1}{x} d x

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

\int 9 d x = 9 x

\int \frac{1}{x} d x = ln ∣ x ∣

= \frac{7 x ^{2}}{2} - 9 x + ln ∣ x ∣

Add a constant to the solution

= \frac{7 x ^{2}}{2} - 9 x + ln ∣ x ∣ + C

What is the integral of (7x^2-9x+1)/x ?
The integral of (7x^2-9x+1)/x is (7x^2)/2-9x+ln|x|+C