JEE Mains · Maths · STD 12 - 7.1 indefinite integral
\(\smallint \frac{{2{x^{12}} + 5{x^9}}}{{{{\left( {{x^5} + {x^3} + 1} \right)}^3}}}dx = \)
- A \(\frac{{{x^5}}}{{2{{\left( {{x^5} + {x^3} + 1} \right)}^2}}} + c\)
- B \(\frac{{ - {x^{10}}}}{{2{{\left( {{x^5} + {x^3} + 1} \right)}^2}}} + c\)
- C \(\frac{{ - {x^5}}}{{{{\left( {{x^5} + {x^3} + 1} \right)}^2}}} + c\)
- D \(\frac{{{x^{10}}}}{{2{{\left( {{x^5} + {x^3} + 1} \right)}^2}}} + c\)
Answer & Solution
Correct Answer
(D) \(\frac{{{x^{10}}}}{{2{{\left( {{x^5} + {x^3} + 1} \right)}^2}}} + c\)
Step-by-step Solution
Detailed explanation
\(\int {\frac{{2{x^{12}} + 5{x^9}}}{{{{\left[ {{x^5}\left( {1 + \frac{1}{{{x^2}}} + \frac{1}{{{x^5}}}} \right)} \right]}^3}}}} = \int {\frac{{2{x^{12}} + 5{x^9}}}{{{x^{15}}{{\left( {1 + \frac{1}{{{x^2}}} + \frac{1}{{{x^5}}}} \right)}^3}}}} dx\) Dividing numerator and denominator…
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