Question

Determinati primitiva functiei f(x) = 1 \4 x^{2} + 1

Answer 1

$\int\limits { \frac{1}{4x^2+1} } \, dx= \frac{1}{4} \int\limits { \frac{1}{x^2+( \frac{1}{2})^2 } } \, dx= \frac{1}{4}*2arctg \frac{x}{ \frac{1}{2} }+C= \frac{1}{2}arctg2x+C$