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Choose the correct answer int(dx)/(x(x...

Choose the correct answer
`int(dx)/(x(x^(2)+1))` equals

A

`logabsx-1/2log(x^(2)+1)+C`

B

`logabsx+1/2log(x^(2)+1)+C`

C

`-logabsx+1/2log(x^(2)+1)+C`

D

`1/2logabsx+log(x^(2)+1)+C`

Text Solution

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The correct Answer is:
A
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NCERT GUJARATI-INTEGRALS-EXERCISE 7.5
  1. Integrate the rational functions x/((x-1)(x-2)(x-3))

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  2. Integrate the rational functions (2x)/(x^(2)+3x+2)

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  3. Integrate the rational functions (1-x^(2))/(x(1-2x))

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  4. Integrate the rational functions x/((x^(2)+1)(x-1))

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  5. Integrate the rational functions x/((x-1)^(2)(x+2))

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  6. Integrate the rational functions (3x+5)/(x^(3)-x^(2)-x+1)

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  7. Integrate the rational functions (2x-3)/((x^(2)-1)(2x+3))

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  8. Integrate the rational functions (5x)/((x+1)(x^(2)-4))

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  9. Integrate the rational functions (x^(3)+x+1)/(x^(2)-1)

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  10. Integrate the rational functions 2/((1-x)(1+x^(2)))

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  11. Integrate the rational functions (3x-1)/((x+2)^(2))

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  12. Integrate the rational functions 1/(x^(4)-1)

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  13. Integrate the rational functions 1/(x(x^(n)+1)) [Hint: multiply nume...

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  14. (cosx)/((1-sinx)(2-sinx)) [Hint : Put sin x = t]

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  15. Integrate the rational functions ((x^(2)+1)(x^(2)+2))/((x^(2)+3)(x^(...

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  16. Integrate the rational functions (2x)/((x^(2)+1)(x^(2)+3))

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  17. Integrate the rational functions 1/(x(x^(4)-1))

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  18. Integrate the rational functions 1/((e^(x)-1)) [Hint : Put e^(x) = t...

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  19. Choose the correct answer int(xdx)/((x-1)(x-2)) equals

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  20. Choose the correct answer int(dx)/(x(x^(2)+1)) equals

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