How To Integrate 1+sin x /1+cos x
Published On :2021-01-28 14:05:00
begin{array}{l} smallint frac{{{bf{1}} + {bf{sin}}x}}{{{bf{1}} + {bf{cos}}x}}{rm{d}}x\\ smallint frac{{1 + sin x}}{{1 + cos x}};; * ;frac{{1 - cosx}}{{1 - cosx}}{rm{d}}x\ smallint frac{{left( {1 + sin x} right)left( {1 - cos x} right)}}{{1 - {{cos }^2}x}}{rm{d}}x\ smallint frac{{1 + sin x - cos x - sin xcos x}}{{{{sin }^2}x}}{rm{d}}x\ smallint frac{1}{{{{sin }^2}x}} + frac{{sin x}}{{{{sin }^2}x}} - frac{{cos x}}{{{{sin }^2}x}} - frac{{sin xcos x}}{{{{sin }^2}x}}dx\ smallint {csc ^2}x + csc x - cot xcsc x - cot x{rm{d}}x\ Rightarrow - cot x + ln left| ; right.csc x - cot xleft| { + csc x - {{ln }^;}left| ; right.sin x} right| + C end{array}