What is the integral of sqrt(x)ln(5x) ?

The integral of sqrt(x)ln(5x) is 2/3 x^{3/2}ln(5x)-4/9 x^{3/2}+C

Popular >

integral of sqrt(x)ln(5x)

\int x ln (5 x) d x

\frac{2}{3} x^{\frac{3}{2}} ln (5 x) - \frac{4}{9} x^{\frac{3}{2}} + C

Solution steps

\int x ln (5 x) d x

Apply Integration By Parts

: \frac{2}{3} x^{\frac{3}{2}} ln (5 x) - \int \frac{2}{3} x^{\frac{1}{2}} d x

= \frac{2}{3} x^{\frac{3}{2}} ln (5 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 (5 x) - \frac{4}{9} x^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} x^{\frac{3}{2}} ln (5 x) - \frac{4}{9} x^{\frac{3}{2}} + C

x \to 2 - lim (6 - 3 x - 3)

\int_{0}^{1} 2 x (8 - x^{2}) d x

x \to - 3 lim (- 3 x)

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

\int_{0}^{0.5} (200 x) d x

What is the integral of sqrt(x)ln(5x) ?
The integral of sqrt(x)ln(5x) is 2/3 x^{3/2}ln(5x)-4/9 x^{3/2}+C