Asked by mathstudent
Integrate: dx/(2x^2 + 4x + 7)
Answers
Answered by
Reiny
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 <sup>-1</sup> [√10(x+1)/5]
are you working at that sophisticated level of integration??
Is this highschool level ??
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 <sup>-1</sup> [√10(x+1)/5]
are you working at that sophisticated level of integration??
Is this highschool level ??
Answered by
Count Iblis
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.
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.
Answered by
mathstudent
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.
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.
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