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

The integral of (x+5)ln(x) is ln(x)((x^2)/2+5x)-1/2 ((x^2)/2+10x)+C

Popular >

integral of (x+5)ln(x)

\int (x + 5) ln (x) d x

ln (x) (\frac{x ^{2}}{2} + 5 x) - \frac{1}{2} (\frac{x ^{2}}{2} + 10 x) + C

Solution steps

\int (x + 5) ln (x) d x

Apply Integration By Parts

: ln (x) (\frac{x ^{2}}{2} + 5 x) - \int \frac{1}{2} (x + 10) d x

= ln (x) (\frac{x ^{2}}{2} + 5 x) - \int \frac{1}{2} (x + 10) d x

\int \frac{1}{2} (x + 10) d x = \frac{1}{2} (\frac{x ^{2}}{2} + 10 x)

= ln (x) (\frac{x ^{2}}{2} + 5 x) - \frac{1}{2} (\frac{x ^{2}}{2} + 10 x)

Add a constant to the solution

= ln (x) (\frac{x ^{2}}{2} + 5 x) - \frac{1}{2} (\frac{x ^{2}}{2} + 10 x) + C

\frac{d}{d x} (e^{x} sin (e^{x}))

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

\frac{d}{d t} (e^{3 c o s (t) + 2 t^{2}})

\frac{\partial}{\partial x} (e^{- 9 x^{2} - 2 y^{2}})

\int sec^{2} (2 x y) d x

What is the integral of (x+5)ln(x) ?
The integral of (x+5)ln(x) is ln(x)((x^2)/2+5x)-1/2 ((x^2)/2+10x)+C