for this type of question, integral by parts should be used . This involves using the formula for intregation by parts:
lets first break apart the x and e10x into two parts - "u" and "v"
where u = x.
however, we need to find the value of v. in order to do this, we can integrate dv/dx in order to get to v.
the value of dv/dx is : e10x
u = x dv/dx = e10x
as seen in the formula, you need to have a value for u, dv, v and du.
therefore in order to get du you must differentiate u:
u = x
du/dx = 1
du = 1dx = dx
du = dx
in order to get v you need to integrate dv/dx:
e10x dx = 1/10 x10x
now that we have both parts, we can put this back into the formula.
xe10x = x * 1/10e10x - 1/10e10x dx
= x /10e10x - 1/100e10x + c