Math

posted by .

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

  • Math -

    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)]

Respond to this Question

First Name
School Subject
Your Answer

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 integrals. …
  2. CALC 2 - Partial Functions!!

    How do I solve Integral of 7/(16-x^2) I know I must break down (16-x^2) into (x+4)(-x+4), but after I do that what is next?
  3. Partial Decompostion Fractions

    Can you please help me with the following questions please, I don't understand them. I know the general rule about them. Write the partial fraction decomposition of the rational expression. (x^2+4x-1)/(x^2+3)^2 (4x^3+4x^2)/(x^2+5)^2
  4. Algebra-Partial Fractions

    Can you please help me with the following questions please, I don't understand them. I know the general rule about them. Write the partial fraction decomposition of the rational expression. (x^2+4x-1)/(x^2+3)^2 (4x^3+4x^2)/(x^2+5)^2
  5. 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?
  6. Maths: Partial Differentiation

    1) If x = rcos theta and y = r sin theta, show that partial r / partial x = cos theta and find partial theta / partial x. 2) If z = sin theta.sin phi.sin gamma, and z is calculated for the values theta = 30degrees, phi = 45 degrees …
  7. partial fractions

    (7x^2-16)/(x^2-2x) solve by using partial fraction decomposition. i cant figure out how to do this because after i split up the bottom the A and B don't end up having an x^2 in order to equal the numerator of the original fraction. …
  8. Math- Partial Fractions

    Decompose the following into partial fractions after factoring the denominator as much as possible. Please show some work so I can understand how you did it. 1)x^2/((x-1)(x^2+5x+4)) 2)(3x^3-5x^2+12x+4)/(x^4-16) 3)1/(x^2 (x+1)^2 ) 4)(x+1)/((x^2+1) …
  9. Calculus

    s=çdx/(4+5cos x). By using t-substitution, i.e. t=tan(x/2) we get cos x=(1-t^2)/(1+t^2) and dx=2dt/(1+t^2). Substituting in s and simplifying, we get s= 2çdt/4(1+t^2)+5(1-t^2)=2çdt/(9-t^2). Using standard result çdx/(a^2-x^2)=1/a*arctanh …
  10. Math Help

    Directions: Decide whether the statements are true or false by using partial fraction decomposition. If the statement is false, show the correct way to decompose the partial fraction. 3/x^2+x-2=-1/x+2+1/x-1

More Similar Questions