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Integration by partial fraction : int(...

Integration by partial fraction :
`int(x^(2)+1)/(x^(4)+1)dx=.....`

A

`(1)/(sqrt(2))tan^(-1)((x^(2)-1)/(2x))+c`

B

`(1)/(sqrt(2))tan^(-1)((x^(2)-1)/(sqrt(2x)))+c`

C

`(1)/(sqrt(2))tan^(-1)((x^(2)-1)/(2sqrt(x)))+c`

D

`(1)/(sqrt(2))tan^(-1)((x^(2)-1)/(sqrt(2)x))+c`

Text Solution

Verified by Experts

The correct Answer is:
D
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KUMAR PRAKASHAN-INTEGRALS -MULTIPLE CHOICE QUESTIONS(MCQS)
  1. Integration by partial fraction : int(dx)/(x[(logx)^(2)+4log(x)-1)])...

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  2. Integration by partial fraction : int(dx)/(x(x^(n)+1))=....

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  3. Integration by partial fraction : int(x^(2)+1)/(x^(4)+1)dx=.....

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  4. Integration by partial fraction : int(x^(2)-1)/(x^(4)+x^(2)+1)dx=...

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  5. Integration by partial fraction : If int (2x^(2)+3*dx)/((x^(2)-1)(x^...

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  6. Integration by partial fraction : int(xdx)/(x^(4)+x^(2)+1)=......

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  7. Integration by partial fraction : int(4e^(x)+6e^(-x))/(9e^(x)-4e^(-x...

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  8. Integration by partial fraction : int (x^(2))/((x sinx+cosx)^(2))dx=...

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  9. Integration by partial fraction : int(dx)/(sinx-cosx+sqrt(2))=....+c

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  10. Integration by partial fraction : int(dx)/(4 sin^(2)x+5cos^(2)x)dx=....

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  11. Integration by partial fraction : int(adx)/(b+ce^(x))=....+c

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  12. Integration by partial fraction : int(5x^(4)+4x^(5))/((x^(5)+x+1)^(2...

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  13. Integration by partial fraction : int(dx)/(x^(4)-1)=....+c

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  14. Integration by partial fraction : int(x^(3)dx)/(x^(2)+a^(2))=....+c

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  15. Integration by partial fraction : int(dx)/(x^(2)(x+1))=x...+c

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  16. Method of integration by parts : int cos^(2)xdx=....

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  17. Method of integration by parts : int tan^(-1)x dx=....

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  18. Method of integration by parts : int [sin(logx)+cos(logx)]dx=....

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  19. Method of integration by parts : int x sin x sec^(3)xdx=....

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  20. Method of integration by parts : int log(x+1)dx=....

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