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

The integral of (ln(sqrt(11x)))/x is 1/4 ln^2(11x)+C

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integral of (ln(sqrt(11x)))/x

\int \frac{ln ( 11 x )}{x} d x

\frac{1}{4} ln^{2} (11 x) + C

Solution steps

\int \frac{ln ( 11 x )}{x} d x

Apply u-substitution

: \int \frac{ln ( u )}{2 u} d u

= \int \frac{ln ( u )}{2 u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int \frac{ln ( u )}{u} d u

Apply u-substitution

: \int v d v

= \frac{1}{2} \cdot \int v d v

Apply the Power Rule

: \frac{v ^{2}}{2}

= \frac{1}{2} \cdot \frac{v ^{2}}{2}

Substitute back

= \frac{1}{2} \cdot \frac{ln ^{2} ( 11 x )}{2}

Simplify

\frac{1}{2} \cdot \frac{ln ^{2} ( 11 x )}{2} : \frac{1}{4} ln^{2} (11 x)

= \frac{1}{4} ln^{2} (11 x)

Add a constant to the solution

= \frac{1}{4} ln^{2} (11 x) + C

x \to 5 lim (cos (\frac{π x}{3}))

\frac{d}{d x} (sin (x - \frac{π}{6}))

\int \frac{x}{( x ^{2} - 1 ) ( x - 2 )} d x

(4 t^{4} + \frac{4}{t ^{4}})^{\frac{1}{4}}

(e^{2 x} + 4) \frac{d y}{d x} = y

What is the integral of (ln(sqrt(11x)))/x ?
The integral of (ln(sqrt(11x)))/x is 1/4 ln^2(11x)+C