Integral Calculus Question 378
Question: $ \int{{{( \frac{x+2}{x+4} )}^{2}}e^{x}dx} $ is equal to
[AMU 2000]
Options:
A) $ e^{x}( \frac{x}{x+4} )+c $
B) $ e^{x}( \frac{x+2}{x+4} )+c $
C) $ e^{x}( \frac{x-2}{x+4} )+c $
D) $ ( \frac{2xe^{x}}{x+4} )+c $
Show Answer
Answer:
Correct Answer: A
Solution:
$ I=\int{{{( \frac{x+2}{x+4} )}^{2}}e^{x}dx} $ $ =\int{e^{x}[ \frac{x^{2}+4x+4}{{{(x+4)}^{2}}} ]},dx $
$ \Rightarrow I=\int{e^{x}[ \frac{x(x+4)}{{{(x+4)}^{2}}}+\frac{4}{{{(x+4)}^{2}}} ],dx} $ $ =e^{x}[ \frac{x}{x+4}+\frac{4}{{{(x+4)}^{2}}} ],dx $ $ =e^{x}( \frac{x}{x+4} )+c $ .
BETA
