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Method of integration by parts : int c...

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

A

`(x^(4))/(4)-(1)/(4)x sin2x-(1)/(8)cos2 x+c`

B

`(x^(4))/(4)+(1)/(4)x sin2x+(1)/(8)cos2 x+c`

C

`(x^(4))/(4)-(1)/(4)x sin2x+(1)/(8)cos2 x+c`

D

`(x^(4))/(4)+(1)/(4)x sin2x+(1)/(8)cos2 x+c`

Text Solution

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The correct Answer is:
B
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KUMAR PRAKASHAN-INTEGRALS -MULTIPLE CHOICE QUESTIONS(MCQS)
  1. Integration by partial fraction : int(x^(3)dx)/(x^(2)+a^(2))=....+c

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

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

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

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

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

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

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

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

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

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

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

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

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

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  15. Method of integration by parts : int (logx)/((x+1)^(2))dx=.....

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  16. If (d)/(dx)f(x)=cos x +sin x and f(0)=2, then f(x)=.....

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

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  18. Method of integration by parts : inte^(x)[tanx-log(cosx)]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 e^(x)((x^(2)+1))/((x+1)^(2))dx=...

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