Calculate the integrals by partial fractions and using the indicated substitution. Show the results you get are the same.

dx/1-x^2; substitution x= sin pheta

I understand how to do the partial fraction part, but not the second part and I don't know how they are similar. Any help would be appreciated on what to do

  1. 👍 0
  2. 👎 0
  3. 👁 62
  1. They want you to do it two ways. The first is to change it to
    dx/[2(1+x)] + dx/[2(1-x)]
    which integrates to
    (1/2)[ln(1+x) - ln(1-x)]
    = (1/2)ln[(1+x)/(1-x)]

    In the substitution method, with x = sin u
    dx = cos u du

    Integral dx/(1-x^2)= cos u du/1-sin^2u
    = Integral du/cos u = Integral (sec u)
    = (1/2)log[(1+sinu)/(1-sinu)]
    = (1/2)log[(1+x)/(1-x)]

    1. 👍 0
    2. 👎 0
    posted by drwls

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calc easy

    Having trouble getting the correct solution. The integral of “x squared” in the numerator and “x squared plus x minus 6” in the denominator. S X2 / (X2 + x – 6) dx Thanks! That's a messy one. According to my table of

    asked by Ang on February 23, 2007
  2. Calculus

    Integral of x sq/(1+x sq) dx I am not sure how to do this, am i supposed to do partial fractions to break it up? Or is it just some simple substitution?

    asked by O_o Rion on December 7, 2009
  3. Binomial

    Help me on this one :( Express y= (7-3x-x^2)/[((1-x)^2)(2+x)] in partial fractions. Hence, prove that if x^3 and higher powers of x may be neglected, then y=(1/8)(28+30x+41x^2) I did the first part of expressing it in partial

    asked by Keira on March 3, 2010
  4. Calculus

    Which of the following integrals can be integrated using partial fractions using linear factors with real coefficients? a) integral 1/(x^4-1) dx b) integral (3x+1)/(x^2+6x+8) dx c) integral x^2/(x^2+4) d) None of these

    asked by Alice on April 7, 2019
  5. calc II

    Express the integrals as the sum of partial fractions and evaluate the integral: (integral of) (x^2)dx/(x-1)(x^2 +2x+1) My work: The above integral is equal to x^2dx/(x+1)^2 (A/x-1) + (B/x+1) + (Cx+D)/(x+1)^2 = x^2 A(x+1)^2 +

    asked by Jenna on December 6, 2009
  6. calculus

    Assuming that: Definite Integral of e^(-x^2) dx over [0,infinity] = sqrt(pi)/2 Solve for Definite Integral of e^(-ax^2) dx over [-infinity,infinity] I don't know how to approach the new "a" term. I can't use u-substitution,

    asked by mathstudent on January 14, 2008
  7. calculus

    Evaluate the following integrals using the given substitutions. (a) (3x^2 + 10x)dx/(x^3 + 5x^2 + 18 , substitution u = x3 + 5x2 + 18; (b)(14x + 4)cos(7x^2 + 4x)dx,substitution u = 7x^2 + 4x.

    asked by Carrolyn on May 27, 2014
  8. Calc II

    Perform long division on the integrand, write the proper fraction as a sum of partial fractions, and evaluate the integral: (integral of) 2y^4dy/y^3 - y^2 + y - 1 After long divison I get: (integral of)2ydy + 2(integral of)dy +

    asked by Jenna on December 6, 2009
  9. Calculus

    which of the following integrals results from making the substitution u=x^3 in orer to find (squiggly vertical line)x^2cos(x^3)dx ~cos u du ~u^2 cos u du ~u^(2/3) cos u du1/3 os u du ~3 cos u du

    asked by Ken on May 11, 2012
  10. Calculus - Integration

    I came across this problem in my homework, and I was wondering if partial fractions would be rational for this problem. Int [(2x)/((x^2)^2)]dx If I don't use partial fractions, what would I use?

    asked by Sean on May 9, 2008

More Similar Questions