A) \[\frac{1}{3}(x+\log x)+c\]
B) \[\frac{1}{3}{{(x+\log x)}^{2}}+c\]
C) \[\frac{1}{3}{{(x+\log x)}^{3}}+c\]
D) None of these
Correct Answer: C
Solution :
Put \[t=x+\log x\Rightarrow dt=\left( 1+\frac{1}{x} \right)\,dx,\] then \[\int_{{}}^{{}}{\frac{(x+1){{(x+\log x)}^{2}}}{x}\,dx}=\int_{{}}^{{}}{{{t}^{2}}dt}=\frac{{{t}^{3}}}{3}+c\] \[=\frac{1}{3}{{(x+\log x)}^{3}}+c.\]
You need to login to perform this action.
You will be redirected in
3 sec
