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

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

integral of xln(sqrt(11)x)

\int x ln (11 x) d x

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

Solution steps

\int x ln (11 x) d x

Expand

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

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

\int x ln (x) d x = \frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}

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

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

Add a constant to the solution

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

x \to \frac{3 π}{2} lim (sin (x))

d er i v a t i v e f (y) = ln (5 x^{2} - x + 1)

\int \frac{v}{3 - 0.001 v ^{2}} d v

\frac{\partial}{\partial x} (y + arctan (\frac{y}{x}))

\frac{\partial}{\partial y} (x^{3} - y^{2})

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