calculus

Integrate: dx/(2x^2 + 4x + 7)

  1. 👍 0
  2. 👎 0
  3. 👁 20
asked by mathstudent
  1. 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 ??

    1. 👍 0
    2. 👎 0
    posted by Reiny
  2. 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.

    1. 👍 0
    2. 👎 0
    posted by Count Iblis
  3. 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.

    1. 👍 0
    2. 👎 0
    posted by mathstudent

Respond to this Question

First Name

Your Response

Similar Questions

  1. Integral calculus

    Please do help solve the followings 1) Integrate e^4 dx 2) Integrate dx/sqrt(90^2-4x^2) 3) Integrate (e^x+x)^2(e^x+1) dx 4) Integrate xe^x2 dx e^4 is a constant. 3) let u= e^x + x du= (e^x + 1)dx 4) let u= x du=dx v= e^x dv= e^x

    asked by Febby-1 on April 13, 2007
  2. calculus

    1) Integrate Cos^n(x) dx 2) Integrate e^(ax)Sinbx dx 3) Integrate (5xCos3x) dx I Will be happy to critique your thinking on these. 1) Derive a recursive relation. 2) Simplest by replacing sin(bx) by Exp[i b x] and taking imaginary

    asked by Febby on April 13, 2007
  3. Calculus

    6.] Replace the integral in exercise 5 (int. (1/ 1 – t) dt a = 0, b = 1/2with ?1/(1+t) dt with a = 0, b = 1, and repeat the four steps. a. integrate using a graphing utility b. integrate exactly c. integrate by replacing the

    asked by Rajeev on October 16, 2011
  4. Calc 1

    integrate from 0 to pi/4 (sec^2x)/((1+7tanx)^2)^1/3 integrate form pi^2/36 to pi^2/4 (cos(x^1/2))/(xsin(x^1/2))^1/2 integrate from 0 to pi/3 (tanx)/(2secx)^1/2

    asked by Frank on November 30, 2012
  5. calculus 2

    Justify, with a written explanation or a mathematical reasoning and with a sketch of at least two different cases, the following properties of integrals: a) If f(x) is less than or equal to g(x) for a

    asked by bobby on September 12, 2012
  6. Integral calculus

    Please can anyone help with the following problems - thanks. 1) Integrate X^4 e^x dx 2) Integrate Cos^5(x) dx 3) Integrate Cos^n(x) dx 4) Integrate e^(ax)Sinbx dx 5) Integrate 5xCos3x dx The standard way to solve most of these

    asked by Febby on April 13, 2007
  7. calculus help please

    dy/dx = 2y^2 Integrating...y=2/3 y^3 + C put 1,-1 into the equation, and solve for C. Then find the y for x=2 if y= a^uhttp://math2.org/math/integrals/tableof.htm see exponential functions. dy/dx=2y^2 and if y=-1 when x=1, then

    asked by bobpursley on December 10, 2006
  8. Mathematics-Integration

    Question: Prove that [integrate {x*sin2x*sin[π/2*cos x]} dx] /(2x-π) } from (0-π) = [ integrate {sin x*cos x*sin[π/2*cos x} dx ] from (0-π). My thoughts on the question: We know that integrate f(x) dx from (0-a) = integrate

    asked by Shenaya on June 8, 2017
  9. Math Integration

    Integrate: f (x)/(2x + 1) dx let f represent integrate sign let u = x, du = dx => dx = du = f (u)/(2u + 1) du = f u (2u + 1)^(-1) du = (1/2)u^2 (ln|2u + 1|) + c = (1/2)x^2 (ln|2x + 1|) + c ...what did I do wrong? The correct

    asked by Anonymous on February 11, 2009
  10. integrate

    integrate du/3u and integrate x/x^2 dx it might be simple...i just need a head start...tnx

    asked by allison on October 8, 2008
  11. Calculus

    How do you integrate [(x^2)(cos(2(x^3)))]? I tried to integrate by parts but I'm going in circles yet again...

    asked by Hannah on February 13, 2009

More Similar Questions