Antiderivative/Integral Help

HWilliams44

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Oct 1, 2013
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I want to evaluate the antiderivative of (1+4(sinx)^2)/(sinx)^2. I think I should use u substitution, and I tried making u=sinx and dx=du/cosx. I worked the problem out, and got the antiderivative of (1+4u^2)/(ucosx). Is my line of thinking correct? If so, what should I do next? Thanks.
 
I want to evaluate the antiderivative of (1+4(sinx)^2)/(sinx)^2. I think I should use u substitution, and I tried making u=sinx and dx=du/cosx. I worked the problem out, and got the antiderivative of (1+4u^2)/(ucosx). Is my line of thinking correct? If so, what should I do next? Thanks.

There is no need for a u-substitution. Forget it.
1+4sin2(x)sin2(x)=csc2(x)+4\displaystyle \dfrac{{1 + 4{{\sin }^2}(x)}}{{{{\sin }^2}(x)}} = {\csc ^2}(x) + 4

You surely know the anti derivative of csc2(x)+4 ???\displaystyle {\csc ^2}(x) + 4~???
 
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