{"result":{"text":"text Let I = ∫ end text fraction numerator straight e to the power of straight x open parentheses 1 plus sin invisible function application straight x close parentheses over denominator open parentheses 1 plus cos invisible function application straight x close parentheses end fraction dx\nequals blank integral fraction numerator straight e to the power of straight x open parentheses 1 plus 2 sin invisible function application straight x over 2 times cos invisible function application straight x over 2 close parentheses over denominator 2 cos squared straight x over 2 end fraction dx\nequals blank integral straight e to the power of straight x open parentheses 1 half sec squared invisible function application straight x over 2 plus tan invisible function application straight x over 2 close parentheses dx\nequals blank 1 half integral straight e to the power of straight x sec squared straight x over 2 dx plus integral straight e subscript II superscript straight x table row tan row straight I end table straight x over 2 dx\nequals blank 1 half integral straight e to the power of straight x sec squared straight x over 2 dx plus straight e to the power of straight x times tan straight x over 2 minus integral sec squared straight x over 2 times 1 half times straight e to the power of straight x dx plus straight C\nequals blank 1 half integral straight e to the power of straight x sec squared straight x over 2 dx plus straight e to the power of straight x tan straight x over 2 minus 1 half minus straight e to the power of straight x sec squared integral straight x over 2 dx invisible function application plus straight C\nintegral fraction numerator straight e to the power of straight x left parenthesis 1 plus sinx right parenthesis over denominator left parenthesis 1 plus cosx right parenthesis end fraction dx blank equals blank straight e to the power of straight x tan straight x over 2 plus straight C space"},"status":"ok"}