The integral `int[2x^[12]+5x^9]/[x^5+x^3+1]^3.dx` is equal to- (A) `x^10 / (2(x^5 + x^3 +1)^2) ` (B) `x^5/ (2(x^5 + x^3 +1)^2) ` (C) `-x^10 / (2(x^5 + x^3 +1)^2) ` (D) `- x^5 / (2(x^5 + x^3 +1)^2) `A. `(x^(10))/(2(x^(5)+x^(3)+1)^(2))+C`B. `(x^(5))/(2(x^(5)+x^(3)+1)^(2))+C`C. `(-x^(10))/(2(x^(5)+x^(3)+1)^(2))`D. `(-x^(5))/((x^(5)+x^(3)+1)^(2))+C`

The integral `int[2x^[12]+5x^9]/[x^5+x^3+1]^3.dx` is equal to- (A) `x^

1.	The integral `int[2x^[12]+5x^9]/[x^5+x^3+1]^3.dx` is equal to- (A) `x^10 / (2(x^5 + x^3 +1)^2) ` (B) `x^5/ (2(x^5 + x^3 +1)^2) ` (C) `-x^10 / (2(x^5 + x^3 +1)^2) ` (D) `- x^5 / (2(x^5 + x^3 +1)^2) `A. `(x^(10))/(2(x^(5)+x^(3)+1)^(2))+C`B. `(x^(5))/(2(x^(5)+x^(3)+1)^(2))+C`C. `(-x^(10))/(2(x^(5)+x^(3)+1)^(2))`D. `(-x^(5))/((x^(5)+x^(3)+1)^(2))+C`
Answer» Correct Answer - A ` I=int(2x^(12)+5x^(9))/((x^(5)+x^(3)+1)^(3))dx` `=int(((2)/(x^(3))+(5)/(x^(6))))/((1+(1)/(x^(2))+(1)/(x^(5)))^(3))dx` ` "Let " 1+(1)/(x^(2))+(1)/(x^(5))=t` ` :. (dt)/(dx)=(-2)/(x^(3))-(5)/(x^(6))` ` :. int(-dt)/(t^(3))=(1)/(2t^(2))+C` `=(1)/(2(1+(1)/(x^(2))+(1)/(x^(5)))^(2))+C` `=(x^(10))/(2(x^(5)+x^(3)+1)^(2))+C`

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