Posted by mathstudent on Sunday, January 6, 2008 at 11:30pm.
Integrate: dx/(2x^2 + 4x + 7)
- calculus - Reiny, Monday, January 7, 2008 at 12:28am
messy, are you sure you typed correctly?
I was hoping the bottom would factor so I could use partial fractions.
the way it stands I ran it through an integration program to get
(√10/10)[tan -1 [√10(x+1)/5]
are you working at that sophisticated level of integration??
Is this highschool level ??
- calculus - Count Iblis, Monday, January 7, 2008 at 9:19am
You can just write the denominator as:
2x^2 + 4x + 7 =
2 (x^2 + 2 x + 7/2) =
2 [(x + 1)^2 + 5/2]
Then you use the fact that the integral of dx/(x^2 + a^2) = 1/a arctan (x/a)
So, the integral is:
1/2 1/sqrt(5/2) arctan[(x+1)/sqrt(5/2)]=
Answer given by Reiny above.
- calculus - mathstudent, Monday, January 7, 2008 at 11:34am
Thanks Reiny + Iblis!
This is from Wiley textbook "Calculus: Early Transcendentals Combined, 8th Edition", section 8.4. I think problem #41 (from memory).
I typed it right. The answer you two wrote matches the book, however I couldn't figure out how to do it. Makes sense now. Thanks
Reiny, thanks for writing that. I feel like an idiot getting stuck on these textbook problems sometimes.
Answer this Question
- Integral calculus - Please do help solve the followings 1) Integrate e^4 dx 2) ...
- calculus - 1) Integrate Cos^n(x) dx 2) Integrate e^(ax)Sinbx dx 3) Integrate (...
- Calculus - 6.] Replace the integral in exercise 5 (int. (1/ 1 – t) dt a = 0, b...
- calculus 2 - Justify, with a written explanation or a mathematical reasoning ...
- Calculus AB - Please help me integrate this equation using partial fractions: ...
- Calculus - How do you integrate [(x^2)(cos(2(x^3)))]? I tried to integrate by ...
- calculus help please - dy/dx = 2y^2 Integrating...y=2/3 y^3 + C put 1,-1 into ...
- calculus - 1) Integrate (e^x+x)^2(e^x+1) dx 2) Integrate xe^x2 dx Let u=(e^x+x) ...
- Calc 1 - integrate from 0 to pi/4 (sec^2x)/((1+7tanx)^2)^1/3 integrate form pi^2...
- integrate - integrate du/3u and integrate x/x^2 dx it might be simple...i just ...