A) \[\frac{1}{2}\cot (2{{e}^{-x}}+5)+c\]
B) \[-\frac{1}{2}\cot (2{{e}^{-x}}+5)+c\]
C) \[2\cot (2{{e}^{-x}}+5)+c\]
D) \[-2\cot (2{{e}^{-x}}+5)+c\]
Correct Answer: A
Solution :
Put \[2{{e}^{-x}}+5=t\Rightarrow -2{{e}^{-x}}dx=dt,\] then \[\int_{{}}^{{}}{{{e}^{-x}}\text{cose}{{\text{c}}^{\text{2}}}(2{{e}^{-x}}+5)\,dx}=-\frac{1}{2}\int_{{}}^{{}}{\text{cose}{{\text{c}}^{\text{2}}}t\,dt}\] \[=\frac{1}{2}\cot t=\frac{1}{2}\cot (2{{e}^{-x}}+5)+c\].You need to login to perform this action.
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