Question

all steps which used to evaluate this sum

Answer 1

$= > l = intigrate \frac{dx}{1 + tanx} \\ \\ = > intigrate \frac{dx}{1 + \frac{sinx}{cosx} } \\ \\ = > intigrate \frac{cosx}{cosx + sinx} dx \\ \\ = > intigrate \frac{2cosx}{2(cosx + sinx)} dx \\ \\ = > intigrate \frac{cosx + sinx + cosx - sinx}{2(cosx + sinx)} dx \\ \\ = > intigrate \frac{1}{2} dx + \frac{1}{2} intigrate \frac{cosx - sinx}{cosx + sinx} dx \\ \\ = > \frac{x}{2} + \frac{1}{2} intigrate \frac{cosx - sinx}{cosx + sinx}$
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» Taking

=> "cosx+sinx = t"

=> (cosx - sinx)dx = dt
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Now,

$= > \frac{x}{2} + intigrate \frac{dt}{t} \\ \\ = > \frac{x}{2} + \frac{1}{2} ln(t) + c \\ \\ = > \frac{x}{2} + \frac{1}{2} ln(cosx + sinx) + c$
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