Question

$\int \frac{(1+\sqrt{tanx})(1+ta{n}^{2}x)}{2tanx}dx$ equal to

• A. $logta{n}^{2}x+\sqrt{tanx}+c$
  
• B. $logta{n}^{2}x+\frac{1}{2\sqrt{tanx}}+c$
  
• C. $log|tanx|+2\sqrt{tanx}+c$
  
• D. $log|tanx|+\sqrt{tanx}+c$

Answer 1

The correct option is A $logta{n}^{2}x+\sqrt{tanx}+c$


$\int \frac{1}{2sinxcosx}dx+\frac{1}{2}\int \frac{\sqrt{tanx}}{sinxcosx}dx=\frac{1}{2}\int \frac{si{n}^{2}x+co{s}^{2}x}{sinxcosx}dx+\frac{1}{2}\int \frac{se{c}^{2}x}{\sqrt{tanx}}dx=log\left(ta{n}^{2}x\right)+\sqrt{tanx}+c$