A) \[\tan y=c{{(1-{{e}^{x}})}^{3}}\]
B) \[{{(1-{{e}^{x}})}^{3}}\tan y=c\]
C) \[\tan y=c(1-{{e}^{x}})\]
D) \[(1-{{e}^{x}})\tan y=c\]
Correct Answer: A
Solution :
It can be written in the form of \[\frac{{{\sec }^{2}}y}{\tan y}dy=-3\frac{{{e}^{x}}}{1-{{e}^{x}}}dx\] \[\int{\frac{{{\sec }^{2}}y}{\tan y}}dy=-3\int{\frac{{{e}^{x}}}{1-{{e}^{x}}}dx}\] Þ \[\log (\tan y)=3\log (1-{{e}^{x}})+\log c\] Þ \[\tan y=c{{(1-{{e}^{x}})}^{3}}\].
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