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Evaluate: inte^x\ ((1+sinx)/(1+cosx))\ d...

Evaluate: `inte^x\ ((1+sinx)/(1+cosx))\ dx`

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`e^{x}(frac{1+sin x}{1+cos x})`
` =e^{x} frac{sin ^{2} frac{x}{2}+cos ^{2} frac{x}{2}+2 sin }{2 cos ^{2} frac{x}{2}}`
` =frac{1}{2} e^{x}[tan frac{x}{2}+1]^{2}`
` =frac{1}{2} e^{2}(1+tan frac{x}{2})^{2}`
` =frac{1}{2} e^{x}[1+tan ^{2} frac{x}{2}+2 tan frac{x}{2}]`
` =frac{1}{2} e^{x}[sec ^{2} frac{x}{2}+2 tan frac{x}{2}]`
` frac{e^{x}(1+sin x) d x}{(1+cos x)}=e^{x}[frac{1}{2} sec ^{2} frac{x}{2}+tan frac{x}{2}]`
Let `tan frac{x}{2}=f(x) Rightarrow f^{prime}(x)=frac{1}{2} sec ^{2} frac{x}{2}`
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