integral ∫ { cosx/ [ sinx +cosx] } dx

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integral  ∫  { cosx / [ sinx +cosx]  } dx

first express the numerator in terms of the denominator and its derivative
split into two integrals ;one  of them is of the form u' / u which will integrate to ln(u)

 PAGE 1 BASIC INTEGRATION

PAGE 2 INTEGRATION BY SUBSTITUTION 

PAGE 3 INTEGRATION BY COMPLETION OF SQUARES

PAGE 4 INTEGRATION BY PARTS

PAGE 5 INTEGRATION BY MANIPULATION OF NUMERATOR IN TERMS OF DENOMINATOR

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