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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-

A

`(x^(10))/(2(1+x^(3)+x^(5))^(4))+c`

B

`(x^(2)+2x)/((x^(5)+x^(3)+1)^(4))+c`

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
C
`I=int(2x^(12)+5x^(9))/((x^(5)+x^(3)+1)^(3))dx`
`=int (((2)/(x^(3))+(5)/(x^(6)))dx)/((1+(1)/(x^(2))+(1)/(x^(5)))^(3))`
`=int (-dt)/(t^(3)), " where " t=1+(1)/(x^(2))+(1)/(x^(5))`
`=(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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CENGAGE ENGLISH-INDEFINITE INTEGRATION-EXERCISES (Single Correct Answer Type)
  1. int(sqrt(x^2+1))/(x^4)dx=

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  2. int (1+2x^(6))/((1-x^(6))^(3//2))dx is equal to

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

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  4. If In=int( lnx)^n dx then In+nI(n-1)

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  5. int e^x {f(x)-f'(x)}dx= phi(x), then int e^x f(x) dx is

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  6. For x >1,int sin^(- 1)((2x)/(1+x^2))dx is equal to

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  7. If int x((ln(x+sqrt(1+x^2)))/sqrt(1+x^2)) dx=asqrt(1+x^2)ln(x+sqrt(1+x...

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  8. Ifintxlog(1+1/x)dx=f(x)log(x+1)+g(x)x^2+A x+C , then f(x)=1/2x^2 (b) ...

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  9. If I=inte^(-x)log(e^x+1)dx ,t h e nIe q u a l a+(e^(-x)+1)log(e^x+1)...

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  10. "If " int x e^(x) cosx dx=ae^(x)(b(1-x)sinx+cx cosx)+d, then

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  11. int x sinx sec^(3)x dx is equal to

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  12. int e^(tan^(-1)x)(1+x+x^2)d(cot^(-1)x) is equal to (a) -e^(tan^(-1)x)...

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  13. int e^(x)((2 tanx)/(1+tanx)+cot^(2)(x+(pi)/(4)))dx is equal to

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  14. int e^(x^4) (x + x^3 +2x^5) e^(x^2) dx is equal to

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  15. The value of integral inte^x(1/(sqrt(1+x^2))+1/(sqrt((1+x^2)^5)))dxi s...

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  16. int e^(x)((x^(2)+1))/((x+1)^(2))dx is equal to

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  17. int ((x+2)/(x+4))^2 e^x dx is equal to

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  18. inte^(tanx)(secx-sinx)dx is equal to

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  19. int(cosec^2x-2005)/cos^[2005]x.dx

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  20. int(1+2x^(2)+(1)/(x))e^(x^(2)-(1)/(x))dx is equal to (a) -x e^(x^(2)...

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