Easy integration question nd get 10 pts?

Question

Q: ∫x^9 dx/( x^2+4)^6 = _______________________?

answer= 1/10(4-(1/x^2))^-5 + c HOW?

Answer 1

Best Answer - Chosen by Asker

∫x^9 dx/( x^2+4)^6
= ∫x^9 dx/x^12(1 + 4/x^2)^6
= ∫dx/[x^3(1 + 4/x^2)^6]

Let 1 + 4/x^2 = t => - 8/x^3 dx = dt

=> Integral
= - (1/8) ∫ t^(-6) dt
= - (1/8) t^-5/(-5) + c
= (1/40) (1 + 4/x^2)^(-5) + c

[I do not understand why all your answers are turning out to be incorrect! Are they the answers given in the text-book or found by you for verification?]

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thx