Integral Calculus Question 439
Question: $ \int_{{}}^{{}}{\frac{f’(x)}{{{[f(x)]}^{2}}}}\ dx= $
Options:
A) $ -{{[f(x)]}^{-1}}+c $
B) $ \log [f(x)]+c $
C) $ {e^{f(x)}}+c $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
Put $ f(x)=t\Rightarrow {f}’(x),dx=dt, $ then $ \int_{{}}^{{}}{\frac{{f}’(x)}{|f(x){{|}^{2}}},dx}=\int_{{}}^{{}}{\frac{1}{t^{2}},dt}=-\frac{1}{t}+c=-\frac{1}{f(x)}+c. $
BETA
