Integral Calculus Question 332
Question: $ \int_{{}}^{{}}{\log x(\log x+2)\ dx=} $
Options:
A) $ x{{(\log x)}^{2}}+c $
B) $ x{{(1+\log x)}^{2}}+c $
C) $ x[1+{{(\log x)}^{2}}]+c $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ I=\int_{{}}^{{}}{\log x(\log x+2),dx} $ Put $ \log x=t\Rightarrow e^{t}=x\Rightarrow e^{t}dt=dx, $ then $ I=\int_{{}}^{{}}{t(t+2)e^{t}dt}=t^{2}.,e^{t}+c=x{{(\log x)}^{2}}+c. $
BETA
