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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Integrate : $\int \large\frac{1}{\sqrt x -\sqrt {x- 8 }}$$dx$

$(a)\;\frac{-1}{12} [x^{3/2}+(x+3)^{3/2}]+c \\(b)\; \frac{-1}{12} [x^{3/2}-(x+3)^{3/2}]+c \\(c)\; \frac{-1}{12} [x^{3/2}+(x+8)^{3/2}]+c\\ (d)\;None$

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1 Answer

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$\sqrt {x} +\sqrt {x+8}$ multiply in numerator & denominator
=> $\int \large\frac{\sqrt x +\sqrt x+8}{(\sqrt x - \sqrt x +8)( \sqrt {x}+ \sqrt x +8 )}$$dx$
=> $\int \large\frac{\sqrt x +\sqrt {x+8}}{x-x-8}$$dx$
=> $\large\frac{-1}{8} \bigg[ x^{3/2} \times \large\frac{2}{3} +\frac{2}{3}$$ (x+8) ^{3/2}\bigg]+c$
$\large\frac{-1}{12} $$[x^{3/2}+(x+3)^{3/2}]+c $
Hence a is the correct answer.
answered Dec 31, 2013 by meena.p
 
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