anonymous
  • anonymous
the indefinite integral i am given is (e^x - 6x^2)/6... i need to evaluate it. please help!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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nowhereman
  • nowhereman
Do you know the integral of e^x and the power rule?
anonymous
  • anonymous
i assume the integral is e^x
anonymous
  • anonymous
i need to use substitution, but i dont know what to substitute... i've tried it a lot already

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nowhereman
  • nowhereman
You don't need to use any elevated integration techniques. If you want to prove that your result is right, just differentiate it and if you get the original integrand, you're fine.
anonymous
  • anonymous
what about the 6 in the denominator? how do i do that? is it just 6x?
nowhereman
  • nowhereman
No, that is just a factor of 1/6 which you can pull-out.
anonymous
  • anonymous
wow.. i got it! thanks! i have another one tho if u are willing to help?
nowhereman
  • nowhereman
Sure :-)
anonymous
  • anonymous
(5-2xe^x)/x
nowhereman
  • nowhereman
Pull that division into the difference and you should have two known integrals.
anonymous
  • anonymous
like (5/x)-((2xe^x)/x)?
nowhereman
  • nowhereman
Yes, and reduce that x in the second term.
anonymous
  • anonymous
ok. then i would need substitution right?
nowhereman
  • nowhereman
For what? You should know the integral of 1/x and e^x and that's all there is.
anonymous
  • anonymous
i dont know the 1/x one. is it natural log?
nowhereman
  • nowhereman
Exactly, sometimes it is defined this way \[\ln x := \int_1^x\frac 1 y \mathrm d y\] but if you have defined it as the inverse function of e^x you could use the inverse-differentiation rule.
anonymous
  • anonymous
i got that one! thanks a lot. this is my last one... (x-2)/(x^2-4x+4)^3..... that requires substitution correct?
nowhereman
  • nowhereman
Yes, a little one :-) but you should first observe that \[x^2 - 4x + 4 = (x-2)^2\]
anonymous
  • anonymous
so i can cancel one of them right away?
nowhereman
  • nowhereman
yes
anonymous
  • anonymous
would it turn into (x-2)^6?
anonymous
  • anonymous
in the denominator
nowhereman
  • nowhereman
Sure, that is just one of the exponentiation rules.
anonymous
  • anonymous
then after the cancellation i am left with 1/(x-2)^5?
nowhereman
  • nowhereman
Right.
anonymous
  • anonymous
now i substitute u=x-2
nowhereman
  • nowhereman
Yes, but as du/dx = 1 if you are a little more experienced you could just do it in your head.
anonymous
  • anonymous
i think it would be 1/((1/6)*(x-2)^6)
nowhereman
  • nowhereman
Not quite, maybe you should write it is \[(x-2)^{-5}\] instead to see it better.
anonymous
  • anonymous
(-1/4)*(x-2)^-4?
nowhereman
  • nowhereman
Yeah, good.
anonymous
  • anonymous
is this website free to use?
nowhereman
  • nowhereman
It costs both of us our time, but you won't have to pay for it ;-)
anonymous
  • anonymous
so y do ppl like u go around and answer questions?
nowhereman
  • nowhereman
I love math and helping other people.
anonymous
  • anonymous
it seems strange that there is no charge for this service. or breech of security
nowhereman
  • nowhereman
I don't know what you mean by breech of security; but the idea of being is just that everyone can ask questions and give answers here. So if I had a question regarding my study, I could ask them too. Only that it seems there are a lot of high-school students here lately :-D
anonymous
  • anonymous
hmm... thats cool. i guess i'm a skeptic. but with quick responses like the ones u gave me i am becoming a believer

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