Well the proof is very big, so i just give u an idea as to how to go abt proving:
d(e^{(nx)})/dx = ne^{nx}
now increment y by a small value such that:
y + \Delta y = e^{(n(x + \Delta x))}
Divide the whole term by y such that:
(\Delta y)/y = [[e^{(n(x + \Delta x))}]/(e^{(nx)})]...
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Oops Sorry, As hurkyl said, I made a mistake in the identity. However the steps are the same. Bring every term to their sine and cosine forms and then proceed with the problem.
Sridhar
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Your question has already been answered...Just scroll up the page a li'l bit and u have the answer there. I have given the step after using tan(a+b) and then the step after substituting tanx = sinx/cosx and then the method to solve the final integral...
I think u understand that cosx dx...
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Try using the expansion of tan (x+y) to simplify tan 2x and tan 3x and try to bring all the three terms in terms of tanx only. Now substitute tanx=sinx/cosx and simplify the expression you get to see the below answer:
I = the integral = I1+I2;
where,
I1 =...