2 years ago
Evaluate each of the following integrals and simplify completely.
int xln (x)dx
int xln (x)dx
1 Answers
Best Answer
bushticketscolorado Staff answered 2 years ago
bushticketscolorado Staff answered 2 years ago
Step 1
The detailed solution is as follows below:
Step 2
int xln (x)dx
=ln (x)int x dx-int ((d)/(dx)(ln x)int xdx)dx
=ln (x)*(x^(2))/(2)-int (1)/(x)*(x^(2))/(2)dx
=(x^(2))/(2)*ln (x)-(1)/(2)int x dx
=(x^(2))/(2)*ln (x)-(1)/(2)*(1)/(2)*x^(2)+C
=(x^(2))/(2)*ln (x)-(x^(2))/(4)+C
where, C is the constant of integration.