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

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

Popular >

integral of (sqrt(x)ln(x))

\int (x ln (x)) d x

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

Solution steps

\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

= \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}}

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

Add a constant to the solution

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

\frac{d}{d x} (π r (x) (x)^{2} h)

\frac{d y}{d x} = \frac{3 x}{2 y}

\int e^{x} ln (e^{x} + 1) d x

\int \frac{x ^{2}}{( 9 - x ^{2} ) ^{- \frac{3}{2}}} d x

\frac{d}{d x} (20 - 20 \cdot 2^{- x})

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