Integral Calculus Question 471
Question: $ \int{x^{x}(1+\log x)dx} $ is equal to
[RPET 2000]
Options:
A) $ x^{x} $
B) $ x^{2x} $
C) $ x^{x}\log x $
D) $ \frac{1}{2}{{(1+\log x)}^{2}} $
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Answer:
Correct Answer: A
Solution:
$ I=\int{x^{x}(1+\log x),dx} $ . Put $ x^{x}=t $ , then $ x^{x}(1+\log x)dx=dt $
$ \therefore I=\int{dt} $
$ \Rightarrow I=t+C $
$ \Rightarrow I=x^{x}+C $ .
BETA
