Math, asked by basakabantika62, 7 months ago

integrate 2cos2x/(1+sin2x)​

Answers

Answered by gaurav2013c
7

Refer to the attached image ❤️

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Answered by talasilavijaya
1

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

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