A) \[-\cos {{e}^{x}}+c\]
B) \[\cos {{e}^{x}}+c\]
C) \[-\text{cosec}\,{{e}^{x}}+c\]
D) None of these
Correct Answer: A
Solution :
\[\int_{{}}^{{}}{{{e}^{x}}\sin ({{e}^{x}})\,dx}\] Put \[{{e}^{x}}=t\] and \[{{e}^{x}}dx=dt,\] the integral reduces to \[\int_{{}}^{{}}{\sin t\,dt}=-\cos t+c=-\cos ({{e}^{x}})+c.\]
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