What is the integral of (4x^3-6x^2-7x)/(x^2) ?

The integral of (4x^3-6x^2-7x)/(x^2) is 2x^2-6x-7ln|x|+C

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integral of (4x^3-6x^2-7x)/(x^2)

\int \frac{4 x ^{3} - 6 x ^{2} - 7 x}{x ^{2}} d x

2 x^{2} - 6 x - 7 ln ∣ x ∣ + C

Solution steps

\int \frac{4 x ^{3} - 6 x ^{2} - 7 x}{x ^{2}} d x

Expand

\frac{4 x ^{3} - 6 x ^{2} - 7 x}{x ^{2}} : 4 x - 6 - \frac{7}{x}

= \int 4 x - 6 - \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 4 x d x - \int 6 d x - \int \frac{7}{x} d x

\int 4 x d x = 2 x^{2}

\int 6 d x = 6 x

\int \frac{7}{x} d x = 7 ln ∣ x ∣

= 2 x^{2} - 6 x - 7 ln ∣ x ∣

Add a constant to the solution

= 2 x^{2} - 6 x - 7 ln ∣ x ∣ + C

What is the integral of (4x^3-6x^2-7x)/(x^2) ?
The integral of (4x^3-6x^2-7x)/(x^2) is 2x^2-6x-7ln|x|+C