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The integral int(2x^(12)+5x^9)/((x^5+x^3...

The integral `int(2x^(12)+5x^9)/((x^5+x^3+1)^3)dx` is equal to: (1) `(-x^5)/((x^5+x^3+1)^2)+C` (2) `(x^(10))/(2(x^5+x^3+1)^2)+C` (3) `(x^5)/(2(x^5+x^3+1)^2)+C` (4) `(-x^(10))/(2(x^5+x^3+1)^2)+C` where C is an arbitrary constant.

A

`(x ^(5))/( 2 (x ^(5) + x ^(3) + 1) ^(2) ) + C`

B

`(x ^(-10))/( 2 (x ^(5) + x ^(3) + 1) ^(2) ) + C`

C

`(x ^(-x5))/( 2 (x ^(5) + x ^(3) + 1) ^(2) ) + C`

D

`(x ^(10))/( 2 (x ^(5) + x ^(3) + 1) ^(2) ) + C`

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Verified by Experts

The correct Answer is:
D
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The integral int(2x^(12)+5x^(9))/((x^(5)+x^(3)+1)^(3))dx is equal to: (1)(-x^(5))/((x^(5)+x^(3)+1)^(2))+C(2)(x^(5)x^(3))/(2(x^(5)+x^(3)+1)^(2))+C(3)(x^(5))/(2(x^(5)+x^(3)+1)^(2))+C(4)(-x^(3)+x^(3))/(2(x^(5)+x^(3)+1)^(2))+C where C is an arbitrary constant.

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))

int((2x^(12)+5x^(9))dx)/((x^(5)+x^(3)+1)^(3))

The integral int(2x^(12)+5x^(9))/((x^(5)+x^(3)+1)^(3))dx is equal to (where C is a constant of integration)

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DISHA PUBLICATION-INTEGRALS -EXERCISE-2 CONCEPT APPLICATOR
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