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Changing back after substitution

  1. Feb 9, 2014 #1
    1. The problem statement, all variables and given/known data

    I've done 1-3 and 10-20, but these give me an extreme headache. Assume I know everything there is to know about integration and the trigonometric and hyperbolic functions.

    Change the following into variables with x with...

    4. (1/4) * sin(z) - (1/12) * sin^3(z) after having substituted with x+1 = 2tan(z);

    5. -coth(z) after having substituted with x+1 = sinh(z);

    6. (3/16) * sinh(2z)+(1/8)z after having substituted with x = cosh(z);

    7. z - coth(z) after having substituted with x = sinh(z);

    8. -(4/3) * cos^3(z) after having substituted with x+1 = 2sin(z);

    9. tan(z) after having substituted with x - 1 = sin(z).

    2.

    2. Relevant equations

    Everything about integration and the hyperbolic and trigonometric functions.

    3. The attempt at a solution

    I experimented with the double angle rules, dividing by cos^2(z)+sin^2(z), and pretty much everything else. If you could just show me the answer to one of those, it'd be greatly appreciated.
     
  2. jcsd
  3. Feb 9, 2014 #2

    haruspex

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    Can you write sin(z) in terms of tan(z)?
     
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