Evaluate: `int(e^x)/(e^(2x)+5e^x+6)dx`

Explanation

`int frac{e^{x} d x}{e^{2 x}+5 e^{x}+6} `

`text { let } e^{x}=t `

`Rightarrow e^{x} dx=d t `

`text { Now, } int frac{e^{x} d x}{e^{2 x}+5 e^{x}+6} `

`=int frac{d t}{t^{2}+5 t+6} `

`=int frac{d t}{t^{2}+5 t+(frac{5}{2})^{2}-(frac{5}{2})^{2}+6} `

`=int frac{d t}{(t+frac{5}{2})^{2}-frac{25}{4}+6} `

`=int frac{d t}{(t+frac{5}{2})^{2}-frac{25+24}{4}} `

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