Question

Integrate 1" title="\int \: \frac{dx}{1 + \sin(x) } " alt="\int \: \frac{dx}{1 + \sin(x) } " align="absmiddle" class="latex-formula"> pls help!

Answer 1

This is ur required result in attachment

Answer 2

$INTEGRATION \\ \\ \\ Given \: expression \: - \: \\ \\ \int \: \frac{dx}{1 + \sin(x) } \\ \\ \int \frac{1}{(1 + \sin(x) } \times \frac{(1 - \sin(x)) }{(1 - \sin(x)) } \: dx \\ \\ \int \: \frac{(1 - \sin(x)) }{(1 - { \sin }^{2} (x))} \: dx \\ \\ \int \: \frac{(1 - \sin(x)) }{ { \cos }^{2}(x) } \: dx \\ \\ \int \: ( \frac{1}{ {cos}^{2}(x) } - \frac{ \sin(x) }{ {cos}^{2} (x)} ) \: dx \\ \\ \int( {sec}^{2} (x) - \sec(x)\tan(x) ) \: dx \\ \\ \int( {sec}^{2} (x) \: dx \: - \int \sec(x)\tan(x) ) \: dx \: \: \\ \\ \\ \: \tan(x) - \sec(x) + C \: \: \: \: \: \: \: \: \: Ans.$