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

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

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

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

4 + x + 4 ln ∣ x ∣ + C

Solution steps

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

Apply Integration By Parts

: 4 + x - \int - \frac{4}{x} d x

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

\int - \frac{4}{x} d x = - 4 ln ∣ x ∣

= 4 + x - (- 4 ln ∣ x ∣)

Simplify

= 4 + x + 4 ln ∣ x ∣

Add a constant to the solution

= 4 + x + 4 ln ∣ x ∣ + C

\frac{\partial}{\partial x} (x yz - z - sin (x + y))

f (x) = ln (\frac{x - 2}{x + 1})

\int x (7 - y)

\int \frac{1}{9 - 4 x ^{2}} d x

\int_{0}^{\infty} f (a + x) d x

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