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Math Help - Another trig sub integration

  1. #1
    Junior Member
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    Another trig sub integration

    Hey

    Im stuck on the last step of another trig sub again...

    Heres the problem: integrate 1/((x^2)*(sqrt(4x^2-9))

    I've sub'd x=3/2sec(theta)

    I get to the point after integrating ..(2sin(theta))/9 and have to sub back in for theta

    I realise theta=sec^-1(2x/3) but do not understand how i can use 2(sin(sec^-1(2x/3))/9 to finish the problem.

    Please help =)
    thanks
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  2. #2
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    Quote Originally Posted by Sam1111 View Post
    Hey

    Im stuck on the last step of another trig sub again...

    Heres the problem: integrate 1/((x^2)*(sqrt(4x^2-9))

    I've sub'd x=3/2sec(theta)

    I get to the point after integrating ..(2sin(theta))/9 and have to sub back in for theta

    I realise theta=sec^-1(2x/3) but do not understand how i can use 2(sin(sec^-1(2x/3))/9 to finish the problem.

    Please help =)
    thanks
    Create a right angled triangle where an interior angle is \theta and the \sec \theta = \frac{2x}{3} or \cos \theta = \frac{3}{2x}. So the adjacent is 3 and the hypotenuse is 2x. The pythagorean thm gives the opposite as \sqrt{4x^2-9} and from here you can pick of the \sin \theta.
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