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Method of integration by parts : If in...

Method of integration by parts :
If `int_(n)=int(sinx)^(n)dx, x in N` then the value `(5I_(4)-6I_(6))` is .....

A

`sin x(cosx^(5)+c`

B

`sin2x-cos2x+c`

C

`(Sin2x)/(8)(cos^(2)2x+1-cos 2x)+c`

D

None of these

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The correct Answer is:
C
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KUMAR PRAKASHAN-INTEGRALS -MULTIPLE CHOICE QUESTIONS(MCQS)
  1. Method of integration by parts : inte^(3x)cos 4xdx=e^(3x)(A sin 4x+B...

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  2. Method of integration by parts : inte^(2x)*x^(4)dx=(e^(2x))/(2)f(x)+...

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  3. Method of integration by parts : If int(n)=int(sinx)^(n)dx, x in N t...

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  4. Method of integration by parts : If I(n)=int cot^(n)x dx then I(0)+I...

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  5. Method of integration by parts : If u=inte^(ax)cos bx dx and v= int ...

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

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  7. Method of integration by parts : int cos(logx)dx=....+c

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  8. Method of integration by parts : inte^(x)sin x cos x dx=...+c

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  9. Integrate the following functions : (5+logx)/((6+logx)^(2))

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  10. int(e^(tan^-1(x)))/(1+x^(2))(1+x+x^(2))dx=...+c

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  11. Integrate the functions e^(x)((1+sinx)/(1+cosx))

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  12. Integrate the following functions : e^(x)((1+xlogx)/(x))

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  13. int(logx+(1)/(x^(2)))e^(x)dx=..........+c

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  14. int(x^(6)+7x^(5)+6x^(4)+5x^(3)+4x^(2)+3x+1)e^(x)dx=.......+c

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  15. intxcos2xdx=.......+c

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  16. intsin^(-1)xdx=......+c

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  17. inte^(x)(cotx-cot^(2)x)dx=.......+c

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  18. int(e^(x))/(x+1)[1+(x+1)log(x+1)]dx=......+c

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  19. int(x-1)/((x+1)^(3))e^(x)dx=.......+c

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  20. If intx.e^(2x)dx=e^(2x)f(x)+c where c is arbitary constant then f(x)=…...

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