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Integration by partial fraction : int(...

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

A

`(1)/(sqrt(5))tan^(-1)((2tanx)/(sqrt(5)))`

B

`(1)/(sqrt(5))tan^(-1)((tanx)/(sqrt(5)))`

C

`(1)/(2sqrt(5))tan^(-1)((2tanx)/(sqrt(5)))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
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KUMAR PRAKASHAN-INTEGRALS -MULTIPLE CHOICE QUESTIONS(MCQS)
  1. Integration by partial fraction : int (x^(2))/((x sinx+cosx)^(2))dx=...

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

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

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

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

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

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

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

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

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

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

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

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

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  14. Method of integration by parts : If int log(x^(2)+x)dx=x log(x^(2)+x...

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  15. Method of integration by parts : int x^(2)sin2x dx=....

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  16. Method of integration by parts : intx^(n)logxdx=....

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  17. Method of integration by parts : int[(1)/(logx)-(1)/((logx)^(2))]dx=...

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  18. int (logx)/((1+logx)^(2))dx=....

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  19. Method of integration by parts : inte^(2x) (1+sin 2x)/(1+cos 2x)dx=....

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  20. Method of integration by parts : int[f(x)g''(x)-f''(x)g(x)]dx=....

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