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Popular >

integral of ((4+u))/u

Solution

\int \frac{( 4 + u )}{u} d u

Solution

4 ln ∣ u ∣ + u + C

Solution steps

\int \frac{4 + u}{u} d u

Expand

\frac{4 + u}{u} : \frac{4}{u} + 1

= \int \frac{4}{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{4}{u} d u + \int 1 d u

\int \frac{4}{u} d u = 4 ln ∣ u ∣

\int 1 d u = u

= 4 ln ∣ u ∣ + u

Add a constant to the solution

= 4 ln ∣ u ∣ + u + C

Graph

Popular Examples

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\int \frac{x}{3 + x} d x

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\int csc^{2} (2 - 3 x) d x

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\int sin (2 θ) cos (θ) d θ

integral of 14xln(7x)

\int 14 x ln (7 x) d x

Frequently Asked Questions (FAQ)

What is the integral of ((4+u))/u ?
The integral of ((4+u))/u is 4ln|u|+u+C