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# Integration problems watch

1. (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?
2. (Original post by bono)
What is cosec, cosh and shine?
cosec is 1/sin sec 1/cos and cot 1/tan 4 sum reason
3. (Original post by bono)
What is cosec, cosh and shine?
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
4. 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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