Respuesta :
Answer:
for this type of question, integral by parts should be used . This involves using the formula for intregation by parts:
intudv=uv-intvdu.
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:
\displaystyle \inte10x dx = 1/10 x10x
now that we have both parts, we can put this back into the formula.
intudv=uv-intvdu.
\displaystyle \intxe10x = x * 1/10e10x - \displaystyle \int1/10e10x dx
Step-by-step explanation:
Answer:
((10x-1)e^(10x))/10 + C
Step-by-step explanation:
10 integral (xe^(10x)) dx
Integrate by parts f=x f'=1 / g'=e^(10x) g= (e^(10x))/10
(xe^(10x)/10) - integral (e^(10x)/10) dx
Solving integral (e^(10x)/10) dx :
1/100 integral (e^u) du
= e^u/1000 = e^(10x)/100
(xe^(10x)/10)-(e^(10x)/100)
10 integral (xe^(10x)) dx
= xe^(10x)- (e^(10x))/10
= xe^10x - (e^(10x))/10 + C
= ((10x-1)e^(10x))/10 + C
