Question

Is the following a correct solution?

Answer 1

\[\int\limits_{}^{}\frac{ 1 }{ 4+x ^{2} }dx=\frac{ (x-\sqrt{4}i) }{ (x+\sqrt{4}i) }\]
\[=\int\limits_{}^{}\frac{u-2\sqrt{4}i}{u}=\int\limits_{}^{}\frac{-2\sqrt{4}i}{u}=-2\sqrt{4}i \ln|u| + c\]
\[=-2\sqrt{4}i \ln|x+\sqrt{4}i| + c\]

Answer 2

i didnt get your solution/or the question..please clarify..

Answer 3

The question is: is \[-2\sqrt{4}i \ln |x+\sqrt{4}i| + c\] the indefinite integral of \[\int\limits_{}^{}\frac{1}{4+x ^{2}} dx\]

Answer 4

you can see
1/ 4+x^2 =
1/ (x+ 2i)(x-2i) = 1/4i * (x+2i - (x-2i))/(x+2i)(x-2i)

now separate(simplify) and integrate..hope that helped..
am sorry i dint get your soln much.