What is the integral of ln(sqrt(11)x) ?

The integral of ln(sqrt(11)x) is xln(x)-x+1/2 ln(11)x+C

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integral of ln(sqrt(11)x)

\int ln (11 x) d x

x ln (x) - x + \frac{1}{2} ln (11) x + C

Solution steps

\int ln (11 x) d x

Simplify

ln (11 x) : ln (x) + \frac{1}{2} ln (11)

= \int ln (x) + \frac{1}{2} ln (11) 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 ln (x) d x + \int \frac{1}{2} ln (11) d x

\int ln (x) d x = x ln (x) - x

\int \frac{1}{2} ln (11) d x = \frac{1}{2} ln (11) x

= x ln (x) - x + \frac{1}{2} ln (11) x

Add a constant to the solution

= x ln (x) - x + \frac{1}{2} ln (11) x + C

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What is the integral of ln(sqrt(11)x) ?
The integral of ln(sqrt(11)x) is xln(x)-x+1/2 ln(11)x+C