JEE Mains · Maths · STD 12 - 7.1 indefinite integral
If \(m\) is a non-zero number and \(\int \frac{x^{5 m-1}+2 x^{4 m-1}}{\left(x^{2 m}+x^{m}+1\right)^{3}} d x=f(x)+c\) , then \(f(x)\) is
- A \(\frac{{{x^{5m}}}}{{2m{{\left( {{x^{2m}} + {x^m} + 1} \right)}^2}}}\)
- B \(\frac{{{x^{4m}}}}{{2m{{\left( {{x^{2m}} + {x^m} + 1} \right)}^2}}}\)
- C \(\frac{{2m\left( {{x^{5m}} + {x^{4m}}} \right)}}{{{{\left( {{x^{2m}} + {x^m} + 1} \right)}^2}}}\)
- D \(\frac{{\left( {{x^{5m}} - {x^{4m}}} \right)}}{{2m{{\left( {{x^{2m}} + {x^m} + 1} \right)}^2}}}\)
Answer & Solution
Correct Answer
(B) \(\frac{{{x^{4m}}}}{{2m{{\left( {{x^{2m}} + {x^m} + 1} \right)}^2}}}\)
Step-by-step Solution
Detailed explanation
\(\int \frac{x^{5 m-1}+2 x^{4 m-1}}{\left(x^{2 m}+x^{m}+1\right)^{3}} d x\) \(=\int \frac{x^{5 m-1}+2 x^{4 m-1}}{x^{6 m}\left(1+x^{-m}+x^{-2 m}\right)^{3}} d x\) \(=\int \frac{x^{-m-1}+2 x^{-2 m-1}}{\left(1+x^{-m}+x^{-2 m}\right)^{3}} d x\) \(\text { Put } t=1+x^{-m}+x^{-2 m}\)…
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