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

$(A) \;\large\frac{x^7}{7}-\large \frac{1}{5 x^5} +x^3-\large \frac{3}{x}+c \\(B) \;\large\frac{x^7}{7} +\large \frac{1}{5 x^5} +x^3-\large \frac{3}{x}+c \\ (C)\; \large\frac{x^7}{7} -\large \frac{1}{5 x^5} -x^3-\large \frac{3}{x}+c \\ (D)\;\large\frac{x^7}{7} +\large \frac{1}{5 x^5} +x^3+\large \frac{3}{x}+c $
Can you answer this question?

1 Answer

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By using algebraic property
=> $(a+b)^3=a^3+b^3+3ab(a-b)$
=> $\int x^6 +\large\frac{1}{x^6}$$+3 \bigg(\large\frac{1}{x^2}$$+x^2\bigg).dx$
=> $\large\frac{x^7}{7} $$-\large \frac{1}{5 x^5} $$+x^3-\large \frac{3}{x}+c$
Hence a is the correct answer.
answered Dec 18, 2013 by meena.p
edited Mar 20, 2014 by balaji.thirumalai
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