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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Integrate : $\int \large\frac{e^x + \cos x }{e^x+ \sin x} $$dx$

\[\begin {array} {1 1} (a)\;\log (e^x+\sin x)+c \\ (b)\;\log (e^x-\sin x)+c \\ (c)\;\log (\sin x-e^x )+c \\ (d)\;None \end {array}\]
Can you answer this question?
 
 

1 Answer

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$e^x + \sin x=t$
$(e^x+ \cos x)dx=dt$
$\int \large\frac{dt}{t}$
=> $\log t +c$
=> $ \log (e^x +\sin x )+c$
Hence a is the correct answer.
answered Dec 19, 2013 by meena.p
 
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