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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

= 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

e x p an d - \frac{z}{e ^{z + 1} ( z - 1 ) ^{2}}

s im pl i f y t^{- 1}

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

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