What is the integral of ((4x^2+7x)/(x^2)) ?

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

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integral of ((4x^2+7x)/(x^2))

\int (\frac{4 x ^{2} + 7 x}{x ^{2}}) d x

4 x + 7 + 7 ln ∣ x ∣ + C

Solution steps

\int \frac{4 x ^{2} + 7 x}{x ^{2}} d x

Apply Integration By Parts

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

\int - \frac{7}{x} d x = - 7 ln ∣ x ∣

= 4 x + 7 - (- 7 ln ∣ x ∣)

Simplify

= 4 x + 7 + 7 ln ∣ x ∣

Add a constant to the solution

= 4 x + 7 + 7 ln ∣ x ∣ + C

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