(\integral\_{}^{}\frac{dx}{\sin x + \sqrt{3}\cos x}) = | MATH - INTEGRATION OF RATIONAL FUNCTION BY USING PARTIAL FRACTIONS, EVALUATION | SolveeIt

$\int_{}^{}\frac{dx}{\sin x + \sqrt{3}\cos x}$ =

log tan $\left( \frac{x}{2} + \frac{\pi}{2} \right)$ + c

$\frac{1}{2}$ log tan $\left( \frac{x}{2} + \frac{\pi}{6} \right)$ + c

log cot $\left( \frac{x}{2} + \frac{\pi}{6} \right)$ + c

$\frac{1}{2}$ log cot $\left( \frac{x}{2} + \frac{\pi}{6} \right)$ + c

Answer

$\frac{1}{2}$ log tan $\left( \frac{x}{2} + \frac{\pi}{6} \right)$ + c

Explanation

= $\frac { 1 } { 2 }$ $\int_{}^{}\frac{dx}{\frac{\sin x}{2} + \frac{\sqrt{3}}{2}\cos x}$

= = $\frac{1}{2}\int_{}^{}{\cos ec\left( x + \frac{\pi}{3} \right)}$

Question: \(\int_{}^{}\frac{dx}{\sin x + \sqrt{3}\cos x}\) =...