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Popular Calculus >

integral of (5+u)/u

Solution

\int \frac{5 + u}{u} d u

Solution

5 ln ∣ u ∣ + u + C

Solution steps

\int \frac{5 + u}{u} d u

Expand

\frac{5 + u}{u} : \frac{5}{u} + 1

= \int \frac{5}{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{5}{u} d u + \int 1 d u

\int \frac{5}{u} d u = 5 ln ∣ u ∣

\int 1 d u = u

= 5 ln ∣ u ∣ + u

Add a constant to the solution

= 5 ln ∣ u ∣ + u + C

Graph

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\int \frac{18}{x} d x

tangent of f(x)=x^2-2x,\at x=3 tangent of

f (x) = x^{2} - 2 x, at x = 3

(\partial)/(\partial y)(e^x+ye^{xy})

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Frequently Asked Questions (FAQ)

What is the integral of (5+u)/u ?
The integral of (5+u)/u is 5ln|u|+u+C