Question

integrate-->
$\frac{cosx}{(1 + sinx)^{2} }$
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Answer 1

Answer:

just substitute 1+sinx =t and differentiate both side and put the the value of t in the function to solve further

Answer 2

Answer:

$\frac{ \cos(x) }{ 1 + \sin(x^{2} ) }$

$= \frac{ \cos(x) }{ {1 + \sin(x) }^{2} } \times \frac{1 - { \sin(x) }^{2} }{1 - { \sin(x) }^{2} }$

$= \frac{cos \: x \: \times 1 - {sin}^{2}x }{1+ {sin}^{2}x \times 1 - {sin}^{2}x }$

${sin}^{2}x + {cos}^{2}x = 1$

$= \frac{ \cos(x) \times { \cos(x) }^{2} }{ {cos}^{2}x } \\ \ = cos(x)$