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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
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$f(x) =\int \large\frac{x^6+1}{x^2+1}$$dx+c,$ then find $f(0)-C=?$

$(a)\;1 \\(b)\;2 \\(c)\; 3 \\ (d)\;4 $

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1 Answer

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$A^3+B^3=(A+B)^3 -3 AB(A+B)$
=> $ (x^2)^3+(1)^3=(x^2+1)^3 -3(x^2)(x^2+1)$
=> $\int \large\frac{(x^2+1)^3-3x^2(x^2+1)}{(x^2+1)}$$dx$
=> $ \int (x^2+1)^2 -3x^2dx$
=> $\int x^4+2x^2+1-3x^2.dx$
=> $\large\frac{x^5}{5} -\frac{x^3}{3} $$+1+c$
Hence a is the correct answer.
answered Dec 31, 2013 by meena.p
 

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