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Popular >

integral of (11+x)/x

Solution

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

Solution

11 ln ∣ x ∣ + x + C

Solution steps

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

Expand

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

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

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}{x} d x + \int 1 d x

\int \frac{11}{x} d x = 11 ln ∣ x ∣

\int 1 d x = x

= 11 ln ∣ x ∣ + x

Add a constant to the solution

= 11 ln ∣ x ∣ + x + C

Graph

Popular Examples

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\int 3 x e^{6 x^{2}} d x

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\int \frac{9}{( 4 + x ^{2} ) ^{3}} d x

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\int \frac{sec ^{2} ( x )}{2 + tan ^{2} ( x )} d x

integral of 9/(xln(7x))

\int \frac{9}{x ln ( 7 x )} d x

integral of 3(3x-2)^5

\int 3 (3 x - 2)^{5} d x

Frequently Asked Questions (FAQ)

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