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∫(3x⁴+4x³/x⁴+x+1)²dx Find the solution in this type of question to related to intigration chapter

  • ∫(3x⁴+4x³/x⁴+x+1)²dx
  • Find the solution  in this type of question to related to intigration chapter 

Question Image
Grade:12

1 Answers

Aditya Gupta
2080 Points
one year ago
Multiply the numerator and denominator by x^-8 to convert the integrand into:
(3x^-4+4x^-5)/(1+x^-3+x^-4)^2.
Now simply substitute y= 1+x^-3+x^-4 so that dy= -(3x^-4+4x^-5)dx.
After that you can easily integrate -y^-2 to get the final answer!

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