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Class 12 Integrals · Mcq Single Correct1 Markssubstitution

Class 12 Maths · Integrals · Mcq Single Correct #121

For x≠0, evaluate \(\int x^9/(4x^2+1)^6dx\).

(A) \(\frac1{5x}(4+x^{-2})^{-5}+C\)
(B) \(\frac15(4+x^{-2})^{-5}+C\)
(C) \(\frac1{10x}(x^{-2}+4)^{-5}+C\)
(D) \(\frac1{10}(x^{-2}+4)^{-5}+C\)

✅ Step-by-Step Solution

Final Answer: Option (D): \(\frac1{10}(x^{-2}+4)^{-5}+C\)

Option d equals x¹⁰/[10(4x²+1)⁵]; its derivative is x⁹/(4x²+1)⁶. The rational primitive also extends through 0.

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