What is the integral of 1+1/u+1/(u^2) ?

The integral of 1+1/u+1/(u^2) is u+ln|u|-1/u+C

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integral of 1+1/u+1/(u^2)

\int 1 + \frac{1}{u} + \frac{1}{u ^{2}} d u

u + ln ∣ u ∣ - \frac{1}{u} + C

Solution steps

\int 1 + \frac{1}{u} + \frac{1}{u ^{2}} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1 d u + \int \frac{1}{u} d u + \int \frac{1}{u ^{2}} d u

\int 1 d u = u

\int \frac{1}{u} d u = ln ∣ u ∣

\int \frac{1}{u ^{2}} d u = - \frac{1}{u}

= u + ln ∣ u ∣ - \frac{1}{u}

Add a constant to the solution

= u + ln ∣ u ∣ - \frac{1}{u} + C

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