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int(x^9)/((4x^2+1)^6) dx is equal to...

`int(x^9)/((4x^2+1)^6) dx` is equal to

A

`(1)/(5x)(4+(1)/(x^(2)))^(-5)+C`

B

`(1)/(5)(4+(1)/(x^(2)))^(-5)+C`

C

`(1)/(10)(1+4x^(2))^(-5)+C`

D

`(1)/(10)(4+(1)/(x^(2)))^(-5)+C`

Text Solution

Verified by Experts

The correct Answer is:
D
`I=int(x^(9)dx)/((4x^(2)+1)^(6))=int(dx)/(x^(3)(4+(1)/(x^(2)))^(6))`
`= -(1)/(2)int(d(4+(1)/(x^(2))))/((4+(1)/(x^(2)))^(6))= -(1)/(2)((4+(1)/(x^(2)))^(-5))/(-5)+C`
`=(1)/(10)(4+(1)/(x^(2)))^(-5)+C`
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CENGAGE-INDEFINITE INTEGRATION-Exercise (Single)
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  2. If int f(x) sinx cosx dx=(1)/(2(b^(2)-a^(2))) "In " f(x)+c," then " f...

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  3. int(x^9)/((4x^2+1)^6) dx is equal to

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  4. If int1/(xsqrt(1-x^3))dx=alog|(sqrt(1-x^3)-1)/(sqrt(1-x^3)+1)|+b ,t h...

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  5. The value of the integral int(x^2+x)(x^(-8)+2x^(-9))^(1/(10))dx is 5/(...

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  6. int(x^3dx)/(sqrt(1+x^2))i se q u a lto 1/3sqrt(1+x^2)(2+x^2)+C 1/3...

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  7. If I=int (dx)/((a^(2)-b^(2)x^(2))^(3//2)), then I equals

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  8. int(x^4-1)/(x^2sqrt(x^4+x^2+1))dx= sqrt(x^2+1/(x^2)+1)+C (sqrt(x^4...

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  9. int(sqrt(x^2+1))/(x^4)dx=

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

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  11. The integral int(2x^(12)+5x^(9))/((x^(5)+x^(3)+1)^(3)) dx is equal to

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

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  13. Let inte^x{f(x)-f^(prime)(x)}dx=varphi(x)dot Then inte^xf(x)dx is varp...

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  14. sin^(-1) ((2x)/(1 + x^(2)))

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  15. 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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  16. 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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  17. 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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  18. "If " int x e^(x) cosx dx=ae^(x)(b(1-x)sinx+cx cosx)+d, then

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

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

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