What is the integral of x^{5/2}ln(x) ?

The integral of x^{5/2}ln(x) is 2/7 x^{7/2}ln(x)-4/49 x^{7/2}+C

Popular >

integral of x^{5/2}ln(x)

\int x^{\frac{5}{2}} ln (x) d x

\frac{2}{7} x^{\frac{7}{2}} ln (x) - \frac{4}{49} x^{\frac{7}{2}} + C

Solution steps

\int x^{\frac{5}{2}} ln (x) d x

Apply Integration By Parts

: \frac{2}{7} x^{\frac{7}{2}} ln (x) - \int \frac{2}{7} x^{\frac{5}{2}} d x

= \frac{2}{7} x^{\frac{7}{2}} ln (x) - \int \frac{2}{7} x^{\frac{5}{2}} d x

\int \frac{2}{7} x^{\frac{5}{2}} d x = \frac{4}{49} x^{\frac{7}{2}}

= \frac{2}{7} x^{\frac{7}{2}} ln (x) - \frac{4}{49} x^{\frac{7}{2}}

Add a constant to the solution

= \frac{2}{7} x^{\frac{7}{2}} ln (x) - \frac{4}{49} x^{\frac{7}{2}} + C

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

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

\frac{d y}{d x} = \frac{1}{y ^{2}}

f (x) = 3 x - 12 x^{3}, at x = 0

\int 4 x 1 + 4 x^{2} d x

What is the integral of x^{5/2}ln(x) ?
The integral of x^{5/2}ln(x) is 2/7 x^{7/2}ln(x)-4/49 x^{7/2}+C