Question

Please solve this ASAP
and please no fake answers
​

Answer 1

$\rm \longrightarrow\displaystyle \large\int \dfrac{1}{ \rm {e}^{x} + {e}^{ - x} } \rm \: dx \\ \\ \\ \rm \longrightarrow\displaystyle\large \int \dfrac{1}{ \rm {e}^{x} + \dfrac{1}{{e}^{ x}} } \rm \: dx \\ \\ \\ \rm \longrightarrow\displaystyle\large \int \dfrac{1}{ \rm \dfrac{{e}^{2x } + 1}{{e}^{ x}} } \rm \: dx \\ \\ \\ \rm \longrightarrow\displaystyle\large \int \dfrac{ \rm{e}^{ x} \: dx}{ \rm{e}^{2 x} + 1 } \\ \\ \rm let \: {e}^{ x} = t \\ \rm {e}^{ x} dx= dt \\ \\ \\ \rm \longrightarrow\displaystyle\large \int \: \rm \dfrac{dt}{ {t}^{2} + 1} \\ \\ \\ \rm \longrightarrow {tan}^{ - 1} t + c \\ \\ \rm now \: put \: t = {e}^{ x}\\ \\ \\ \rm \longrightarrow {tan}^{ - 1} {e}^{ x} + c$

Answer 2

Answer:

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