`inte^(x)((1+sinx)/(1+cosx))dx=?`

1.	`inte^(x)((1+sinx)/(1+cosx))dx=?`
Answer» Correct Answer - `e^(x)"tan"(x)/(2)+C` `I=inte^(x){(1)/(2cos^(2)(x//2))+(2sin(x//2)cos(x//2))/(2cos^(2)(x//2))}dx` `=inte^(x)*{(1)/(2)"sec"^(2)(x)/(2)+"tan"(x)/(2)}dx=e^(x){"tan"(x)/(2)+(1)/(2)sec^(2)(x)/(2)}dx=e^(x)"tan"(x)/(2)+C`.

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