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If I(n)=int (logx)^(n)dx, then the valu...

If `I_(n)=int (logx)^(n)dx`, then the value of `(I_(n)+nI_(n-1))` is -

A

`(log x)^(n-1)+c`

B

`n(logx)^(n)+c`

C

`(x log x)^(n)+c`

D

`x(log x)^(n)+c`

Text Solution

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The correct Answer is:
D
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CHHAYA PUBLICATION-MCQ ZONE -Question Paper 6
  1. The value of the integral int x^(3)log x dx is equal to -

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  2. The value of int(-(1)/(2))^((1)/(2)){[x]+log((1+x)/(1-x))}dx is equal...

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  3. If I(n)=int (logx)^(n)dx, then the value of (I(n)+nI(n-1)) is -

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  4. The value of int(0)^(oo) (x dx)/((1+x)(1+x^(2))) is equal to -

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  5. The value of int (e^(x)dx)/((e^(x)+2)(e^(x)+1)) is equal to -

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  6. The value of int(dx)/(cosx-sinx) is equal to -

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  7. The value of int(0)^((pi)/(2)) ((sinx+cosx)^(2))/(sqrt(1+sin2x))dx is ...

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  8. If int(0)^(pi) x f(sinx) dx=A int(0)^((pi)/(2))f(sinx)dx, then the va...

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  9. The value of int ((x-x^(3))^((1)/(3)))/(x^(4)) dx is equal to -

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  10. The value of int e^(x log a)*e^(x)dx is equal to -

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  11. The value of int(-(pi)/(4))^((pi)/(4)) x^(3) sin^(4) x dx is equal to...

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  12. If f(x)=cosx-cos^(2)x+cos^(3)x-…oo, then the value of int f(x) dx is...

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  13. The value of int(0)^(1)(xdx)/((x+sqrt(1-x^(2)))sqrt(1-x^(2))) is equal...

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  14. The value of int(0)^(2a) (f(x))/(f(x)+f(2a-x))dx is equal to -

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  15. The value of int{(logx-1)/(1+(logx)^(2))}^(2)dx is equal to -

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  16. The value of int(pi)^(2pi)[ 2 cos x]dx is equal to -

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  17. The order and degree of the differential equation [1+((dy)/(dx))^(2)]...

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  18. The differential equation of the system of circles touching the y-axi...

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  19. The integrating factor of the differential equation cosx(dy)/(dx)+y si...

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  20. The general solution of y^(2)dx+(x^(2)-xy+y^(2))dy=0 is -

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