anonymous
  • anonymous
∫[(e^x)/(e^(2x)+3e^x+2),]
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
lokisan u are you replying?
anonymous
  • anonymous
The denominator can be factored as\[(e^x+1)(e^x+2)\]If you then set \[u=e^x \rightarrow du=e^x dx\]you'll end up with\[I=\int\limits_{}{}\frac{e^x}{e^{2x}+3e^x+2}dx=\int\limits_{}{}\frac{du}{(u+1)(u+2)}\]You can use partial fraction decomposition on this last expression:\[\frac{1}{(u+1)(u+2)}=\frac{A}{u+1}+\frac{B}{u+2}\]to find\[A=1, B=-1\]Your integral is then\[I=\int\limits_{}{}\frac{1}{u+1}-\frac{1}{u+2}du = \log (u+1)-\log(u+2)+c\]Substituting back,\[I=\log \frac{e^x+1}{e^x+2}+c\]
anonymous
  • anonymous
is this the answer?

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anonymous
  • anonymous
Yes
anonymous
  • anonymous
thank you. this looks so similar to what we are doing
anonymous
  • anonymous
np - I'd appreciate another fan :P
anonymous
  • anonymous
Whenever you see a polynomial in the denominator, try to factor it. Then try to see if you can use partial fraction decomposition.
anonymous
  • anonymous
how do you become a fan? you are a lifesaver. My evil calculas teacher gave us a take home test even i missed the whole week. thank you and can you help with other problems?
anonymous
  • anonymous
there should be a link next to my name - a blue line saying, "Become a fan". If it's not there, maybe try refreshing you page.
anonymous
  • anonymous
dichalao, what the hell's up with your professor giving you that question? It's an algebraic pain.
anonymous
  • anonymous
she's evil
anonymous
  • anonymous
How many more questions do you have?
anonymous
  • anonymous
I have 10 out of which i have done like 3 . 3 of them are set up only using fraction decomposition. and 2 are solving using decomposition
anonymous
  • anonymous
You may want to spread those questions around (i.e. keep making new posts) so others can help too.
anonymous
  • anonymous
do you know how can i type the equation easily like you did in the reply?
anonymous
  • anonymous
There's a button below, "Equation". You can enter things in there.
anonymous
  • anonymous
sorry but can you show the decomposition part?
anonymous
  • anonymous
Loki do u have time to help me out on that problem?
anonymous
  • anonymous
no in the first answer. you said a=1 b=-1
anonymous
  • anonymous
Yes dichalao...just let me finish here and I'll go back.
anonymous
  • anonymous
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anonymous
  • anonymous
In partial fraction decomposition, you set it out like that when you have linear factors in the bottom. You then multiply both sides by (u+1)(u+2) and you'll end up with 1 on the left and what you see on the right. You need to find A and B that will make the statement true; that is, by comparing coefficients on the left and right.
anonymous
  • anonymous
thanks

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