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Question

[integral from 0 to t]xe^-xdx

this is one of the questions from my calculus online course there are no similar examples to this in the given notebookk

i have taken the first year calculus but forgot somestuff, this was 3 years ago, this is why i really need help!!!

Hints is fine as long of course they lead me to the solution.

This is what i thought i can do , rearrange the equation to somthing like x/e^x dx but now what if i use substitution say u= e^x then du= e^xdx

now the new limits would go like this whwen x= 0 then u= 1 and when the upper limit x=t then u=e^t i think so far so good, i hope someone can confirm the aligibility of this ??!!!

Then :

[integral from 0 to t]x/e^xdx

=[integral from 1 to e^t]x/u[1/e^x]du

now i dont know what to do:uhh: :uhh:

Another question:

is there a specific method for calculation integrals like this????

[integral from 2 to 3 ] 1/[x-1][x-4]dx

also [integral from 0 to 3] 1/([9-x^2]^1/2) dx

Last but not least is there a website anyoone suggests that has examples of such problems???Thank you for the help

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# Problems with calculating integrals

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