Question

integrate 2cos2x/(1+sin2x)​

Answer 1

Refer to the attached image ❤️

Answer 2

Answer:

$\int\limitsb {\frac{2cos2x}{1+sin2x} } \, dx=ln|{1+sin2x}| +c$

Step-by-step explanation:

Given $I=\int\limitsb {\frac{2cos2x}{1+sin2x} } \, dx$

Let ${1+sin2x} =u$, then

                                   $\frac{du}{dx}= 2cos2x \implies 2cos2x.dx =du$

Substituting in $I$, we get

                                     $\int {\frac{2cos2x}{1+sin2x} } \, dx=\int\frac{du}{u}$

                                                        $=ln|{u}|+c$

                                                        $=ln|{1+sin2x}| +c$

Therefore, $\int\limitsb {\frac{2cos2x}{1+sin2x} } \, dx=ln|{1+sin2x}| +c$