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i am suddenly stuck when differentiating. are my concepts right?

if we integrate cosx/sinx, then since cosx is the differentiated form of sinx, then integrating d(sinx)/sinx = ln|sinx|

so now, if i have : integrate z/(1-z^{2})^{1/2}

since z is the differentiated form of the denominator(barring the minus sign), (1-z^{2})^{1/2},

then integrating d((1-z^{2})^{1/2})/(1-z^{2})^{1/2},

shouldn't i get ln (1-z^{2})^{1/2}? but the answer is without the ln, and true enough when i try to differentiate the ln (1-z^{2})^{1/2}, i don't get back my original function.

so where did i go wrong?

thanks!

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# Homework Help: Differentiation concept problem

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