Question

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

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

Answer 1

The correct option is A $\frac{1}{2}\left(logtanx\right)+\sqrt{tanx}+c$

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