Question

the indefinite integral of 1/(sqrt4+x^2)

Answer 1

Let \(x=2\tan u\), so \(dx=2\sec^2u~du\).

Answer 2

then what do i do

Answer 3

\[\int\frac{2\sec^2u}{\sqrt{4+(2\tan u)^2}}~du\\
\int\frac{2\sec^2u}{\sqrt{4+4\tan ^2u}}~du\\
\int\frac{2\sec^2u}{\sqrt4\sqrt{1+\tan ^2u}}~du\\
\int\frac{\sec^2u}{\sqrt{1+\tan ^2u}}~du\]
What's \(1+\tan^2u\) equal to?