indefinite integral

i have know idea on how to do this problem:

int csc^{2}(2t)} / sqrt{1 + cot(2t)} dt

Quote:

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Originally Posted by viet

i have know idea on how to do this problem:

int csc^{2}(2t)} / sqrt{1 + cot(2t)} dt

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Is the integrand not very closly related to the derivative of sqrt(1+cot(2t)) ?
In which case the Fundamental Theorem of Calculus will give the integral.

Unless I have made some elemenatry mistake:

d/dt sqrt(1+cot(2t))=(1/2) 2 (-csc^2(2t))/sqrt(1+cot(2t))=-csc^2(2t)/sqrt(1+cot(2t))

so:

int csc^{2}(2t)} / sqrt{1 + cot(2t)} dt = -sqrt(1+cot(2t))

RonL

-1/2*4^(1/2)*((sin(2*t)+cos(2*t))/sin(2*t))^(1/2)

... i think.