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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Integrate : $\int \large\frac{1}{x+\sqrt x}$$dx$

$(a)\;2 \log (\sqrt x +1)+c \qquad(b)\;2 \log (\sqrt {x +1})+c \qquad(c)\;2 \log (x +1)+c \qquad (d)\;2 \log (\sqrt x +2)+c$
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1 Answer

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$\int \large\frac{1}{\sqrt x} \times \frac{1}{(\sqrt x +1)}$
$\sqrt x +1=t$
$\large\frac{1}{2 \sqrt x }$$dx=dt$
=> $\large\frac{1}{\sqrt x }$$dx=2dt$
=>$\int \large\frac{1}{t} $$.2. dt$
=> $2 \log _e |t|+c$
$2 \log (\sqrt x +1)+c$
Hence a is the correct answer.
answered Dec 24, 2013 by meena.p
 
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