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sir please help me in finding the integral of ∫ dx/(1+tanx).

sir please help me in finding the integral of 
    ∫  dx/(1+tanx).

Grade:12

1 Answers

Aditya Gupta
2086 Points
5 years ago
write it as cosx/(cosx+sinx)= ½*[1+(cosx-sinx)/(cosx+sinx)]
now take ½ out and then you can easily integrate 1.
to integrate (cosx-sinx)/(cosx+sinx), simply put cosx+sinx=y so that dy= (cosx-sinx)dx
so final answer is
½*[x+ln|cosx+sinx|]+C

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