Question

Now, if
u = tan^(−1)2x, then (1/2)int tan^(−1)2x/1 + 4x dx= u du

Answer 1

ok... something wrong about it...
did you mean .../(1+4x^2)...?

Answer 2

never mind i got it thanks

Answer 3

I assume that you mean:
\[\int\limits_{ }^{}\arctan(2x)/(1+4x^2) dx=1/2\int\limits_{ }^{}udu=1/4 u^2 +const=...\]
good Luck!

Answer 4

this is 1/2arctan(2x)^2+C