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Popular >

integral of (6+u)/u

Solution

\int \frac{6 + u}{u} d u

Solution

6 ln ∣ u ∣ + u + C

Solution steps

\int \frac{6 + u}{u} d u

Expand

\frac{6 + u}{u} : \frac{6}{u} + 1

= \int \frac{6}{u} + 1 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 \frac{6}{u} d u + \int 1 d u

\int \frac{6}{u} d u = 6 ln ∣ u ∣

\int 1 d u = u

= 6 ln ∣ u ∣ + u

Add a constant to the solution

= 6 ln ∣ u ∣ + u + C

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Frequently Asked Questions (FAQ)

What is the integral of (6+u)/u ?
The integral of (6+u)/u is 6ln|u|+u+C