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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Integrate : $\int \large\frac{(1-2x^2)^2}{x^{3/2}}$$dx$

\[\begin {array} {1 1} (a)\;\frac{1}{\sqrt x} \bigg[-2+ \frac{8}{7}x^3+\frac{8}{3}x^2 \bigg]+c \\ (b)\;\frac{1}{\sqrt x} \bigg[-2+ \frac{8}{7}x^4-\frac{8}{3}x^3\bigg]+c \\ (c)\;\frac{1}{\sqrt x} \bigg[-2+ \frac{8}{7}x^4-\frac{8}{3}x^2\bigg]+c \\ (d)\;None \end {array}\]

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1 Answer

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$\int \large\frac{1+ 4x^4 -4x^2}{x^{3/2}}$$dx$
=> $ \int x^{-3/2}+4x^{5/2}-4x^{1/2}.dx$
=> $ -2x^{-1/2}+\frac{8}{7}x^{7/2}-\frac{8}{3}x^{3/2}+c$
=> $ \large\frac{-2}{\sqrt x} +\frac{8}{7} $$x^{7/2}-\large\frac{8}{3}$$ x^{3/2} +c$
=>$\bigg[-2+ \frac{8}{7}x^{\Large\frac{7}{2}+\frac{1}{2}}-\frac{8}{3}x^{\Large\frac{3}{2}+\frac{1}{2}}\bigg]$$x \large\frac{1}{\sqrt x}$$+c$
$\large\frac{1}{\sqrt x} \bigg[$$-2+\large \frac{8}{7}x^4-\frac{8}{3}x^2\bigg]+c$
Hence c is the correct answer.
answered Dec 19, 2013 by meena.p
 
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