A) \[\frac{2}{3}{{(1+\log x)}^{3/2}}+c\]
B) \[{{(1+\log x)}^{3/2}}+c\]
C) \[2\sqrt{1+\log x}+c\]
D) \[\sqrt{1+\log x}+c\]
Correct Answer: C
Solution :
Put \[t=1+\log x\Rightarrow dt=\frac{1}{x}dx\], then \[\int_{{}}^{{}}{\frac{dx}{x\sqrt{1+\log x}}}=\int_{{}}^{{}}{\frac{dt}{{{t}^{1/2}}}=2{{t}^{1/2}}+c}=2{{(1+\log x)}^{1/2}}+c\].
You need to login to perform this action.
You will be redirected in
3 sec
