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

The integral of sqrt(11x)ln(x) is sqrt(11)(2/3 x^{3/2}ln(x)-4/9 x^{3/2})+C

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integral of sqrt(11x)ln(x)

\int 11 x ln (x) d x

11 (\frac{2}{3} x^{\frac{3}{2}} ln (x) - \frac{4}{9} x^{\frac{3}{2}}) + C

Solution steps

\int 11 x ln (x) d x

11 x = 11 x

= \int 11 x ln (x) d x

Take the constant out:

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

= 11 \cdot \int x ln (x) d x

Apply Integration By Parts

: \frac{2}{3} x^{\frac{3}{2}} ln (x) - \int \frac{2}{3} x^{\frac{1}{2}} d x

= 11 (\frac{2}{3} x^{\frac{3}{2}} ln (x) - \int \frac{2}{3} x^{\frac{1}{2}} d x)

\int \frac{2}{3} x^{\frac{1}{2}} d x = \frac{4}{9} x^{\frac{3}{2}}

= 11 (\frac{2}{3} x^{\frac{3}{2}} ln (x) - \frac{4}{9} x^{\frac{3}{2}})

Add a constant to the solution

= 11 (\frac{2}{3} x^{\frac{3}{2}} ln (x) - \frac{4}{9} x^{\frac{3}{2}}) + C

f (x) = - \frac{2}{x ^{3}}

\int (1 - x^{2})^{- 0.5} d x

- \frac{z}{e ^{z + 1} ( z - 1 ) ^{2}}

\frac{d}{d x} (x^{2} + 2 x - x^{- 1} + x^{- 3})

h^{^{'}} = 2 t^{2} - 3 e^{t}

What is the integral of sqrt(11x)ln(x) ?
The integral of sqrt(11x)ln(x) is sqrt(11)(2/3 x^{3/2}ln(x)-4/9 x^{3/2})+C