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    (Original post by Nylex)
    That is what I got. I couldn't differentiate last night and so thought it was wrong.

    Thanx .
    What is cosec, cosh and shine? :confused:
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    (Original post by bono)
    What is cosec, cosh and shine? :confused:
    cosec is 1/sin sec 1/cos and cot 1/tan 4 sum reason
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    (Original post by bono)
    What is cosec, cosh and shine? :confused:
    cosh and sinh are hyperbolic functions,
    sinh = (e^x - e^-x)/2
    cosh =( e^x + e^-x)/2
    tanh = sinh/cosh

    Also,
    cosh ix = cos x
    sinh ix = i sin x
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    1) integral dx/(x^2)(1+x^2)^1/2

    becomes

    integral du/sinh^2 u
    = -coth u
    = -cosh u/sinh u
    = -(1+x^2)^1/2/x

    3) integral ln(x+(1+x^2)^1/2)dx
    =xln(x+(1+x^2)^1/2) - integral x(1+x(1+x^2)^(-1/2))/(x+(1+x^2)^1/2)
    =xln(x+(1+x^2)^1/2) - integral x((1+x^2)^1/2 + x)/(x+(1+x^2)^1/2)(1+x^2)^1/2
    =xln(x+(1+x^2)^1/2) - integral x/(1+x^2)^1/2
    =xln(x+(1+x^2)^1/2) - (1+x^2)^1/2
 
 
 
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