Question

I need to find the indefinite integral of 2/(1 + 4x^2). I have looked through every example in my textbook and every note from class, as well as asked another student in the class, and cannot find how to do this.

Answer 1

look at arctan
all you need to do to use arctan formula is substitution:
2x=u
try it & let me know

Answer 2

\[=\int\limits_{ }^{}2dx/(1+4x ^{2})=\int\limits_{}^{}du/(1+u ^{2})=\arctan u=\arctan (2x)+ const\]