`(e^y+1)cosx dx+e^ysinx dy=0`

Explanation

`(e^{y}+1) cos x d x+e^{y} sin x d y=0`


`Rightarrow e^{y} sin x d y=-(e^{y}+1) cos x d x`


`Rightarrow frac{e^{y}}{e^{y}+1} d y=-frac{cos x}{sin x} d x`


`Rightarrow frac{e^{y}}{e^{y}+1} d y=-cot x d x`


Integrate both sides


`int frac{e^{y}}{e^{y}+1} d y=-int cot x d x`


Assume: `e^{y}+1=t`,


Put value in equation, we get


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