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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1
∫  (2x12+  5x9)(x5+  x3+  1)3    dx\int \,\,\frac{{\left( {2{x^{12}} + \,\,5{x^9}} \right)}}{{{{\left( {{x^5} + \,\,{x^3} + \,\,1} \right)}^3}}}\,\,\;dx is equal to
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Correct option: B
x102  (x5+  x3  +1)2  +  c\frac{{{x^{10}}}}{{2\,\,{{\left( {{x^5} + \,\,{x^3}\,\, + 1} \right)}^2}}}\,\, + \,\,c
Option B (x102  (x5+ x3 +1)2 + c\frac{{{x^{10}}}}{{2\,\,{{\left( {{x^5} + \,{x^3}\, + 1} \right)}^2}}}\, + \,c\) is correct because after substituting and integrating, we obtain the given result.

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