What is the integral of sqrt(x)ln(8x) ?

The integral of sqrt(x)ln(8x) is 2/3 x^{3/2}ln(8x)-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

Popular >

integral of sqrt(x)ln(8x)

\int x ln (8 x) d x

\frac{2}{3} x^{\frac{3}{2}} ln (8 x) - \frac{4}{9} x^{\frac{3}{2}} + C

Solution steps

\int x ln (8 x) d x

Apply Integration By Parts

= \frac{2}{3} x^{\frac{3}{2}} ln (8 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}}

= \frac{2}{3} x^{\frac{3}{2}} ln (8 x) - \frac{4}{9} x^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} x^{\frac{3}{2}} ln (8 x) - \frac{4}{9} x^{\frac{3}{2}} + C

y^{'} = 0.0016 y (2500 - y)

y^{^{'}} - y = 6 t e^{2 t}

f (x) = 1 - 4 x, at x = - 1

(x + x) \frac{d y}{d x} = y + y

(2 x y^{2} + 7 y) + (2 x^{2} y + 7 x) y^{^{'}} = 0

What is the integral of sqrt(x)ln(8x) ?
The integral of sqrt(x)ln(8x) is 2/3 x^{3/2}ln(8x)-4/9 x^{3/2}+C