Question

integration of x.dx/1+sinx​

Answer 1

$\int \frac{x}{1 + \sin(x) }dx \\ \int \frac{x(1 - \sin(x)) }{ { \cos(x) }^{2} } dx \\ \int \: x { \sec(x) }^{2}dx - \int \: x \tan(x) \sec(x) dx \\ x \tan(x) - { \sec(x) }^{2} + x \sec(x) - \sec(x) \tan(x) + c</p><p>\\x(tanx + secx)- secx(tanx + secx)\\(tanx + secx)(x - secx)$

Use ILATE formula to solve this question .

Answer 2

Step-by-step explanation:

$\: \: \: \: \: \frac{dx}{1 + \sin(x) } \\ = \tan(x ) - \sec(x) + c$

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