Find and hence find .
I can find , but I don't know how to hence find the integral. We've covered (in the context of this forum) basic integration techniques in class, but not inverse tan. I looked up how to do it in general, but my confusion arises from the wording -- hence -- which suggests that I should be able to figure it out from the derivative. Any help is greatly appreciated.
Let's see:
f(x) = x*arctan(x) so
f'(x) = arctan(x) + x/(1+x^2)
Then,
arctan(x) = f'(x) - x/(1+x^2)
Integrating both sides with respect to x, we should have
S arctan(x)dx = f(x) - (1/2)ln(1+x^2)
Now, plug in x=0 and 1 and do the subtraction. xD