A) \[\tan ({{e}^{x}})+k\]
B) \[\tan ({{e}^{x}})\ .\ e+k\]
C) \[{{e}^{x}}\tan x+k\]
D) \[\frac{\tan ({{e}^{x}})}{{{e}^{x}}}+k\]
Correct Answer: A
Solution :
\[I=\int_{{}}^{{}}{{{e}^{x}}{{\sec }^{2}}({{e}^{x}})\,dx}\]. Put \[{{e}^{x}}=t\Rightarrow {{e}^{x}}dx=dt\] \[\therefore \,\,\,I=\int_{{}}^{{}}{{{\sec }^{2}}t\,dt=\tan t+k=\tan ({{e}^{x}})+k}\].You need to login to perform this action.
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