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Popular >

integral of (11+u)/u

Solution

\int \frac{11 + u}{u} d u

Solution

11 ln ∣ u ∣ + u + C

Solution steps

\int \frac{11 + u}{u} d u

Expand

\frac{11 + u}{u} : \frac{11}{u} + 1

= \int \frac{11}{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{11}{u} d u + \int 1 d u

\int \frac{11}{u} d u = 11 ln ∣ u ∣

\int 1 d u = u

= 11 ln ∣ u ∣ + u

Add a constant to the solution

= 11 ln ∣ u ∣ + u + C

Graph

Popular Examples

integral from 0 to 9 of sqrt(81+x^2)

\int_{0}^{9} 81 + x^{2} d x

integral of 1/(sqrt(441+x^2))

\int \frac{1}{441 + x ^{2}} d x

integral of-(x^3)/4

\int - \frac{x ^{3}}{4} d x

integral of (x^2+x)e^x

\int (x^{2} + x) e^{x} d x

limit as x approaches 0 of (1-9x)^{1/x}

x \to 0 lim ((1 - 9 x)^{\frac{1}{x}})

Frequently Asked Questions (FAQ)

What is the integral of (11+u)/u ?
The integral of (11+u)/u is 11ln|u|+u+C