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If I(n) = int (log x)^(n) dx then I(6) ...

If `I_(n) = int (log x)^(n)` dx then `I_(6) + 6I_(5)` =

A

`x(logx)^(5) + c`

B

`- x(log x)^(5)+ c`

C

`x (log x)^(6) + c`

D

`- x(log x)^(6)+ c`

Text Solution

Verified by Experts

The correct Answer is:
C
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AAKASH SERIES-INDEFINITE INTEGRALS -EXERCISE -II
  1. If I(m.n) = int sin^(m) x cos^(n) xdx then I(5,4) =

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  2. If I(n) = int (e^(ex))/(x^(n)) " dx then " I(n) - (a)/(n-1) .I(n-1) =

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  3. If I(n) = int (log x)^(n) dx then I(6) + 6I(5) =

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  4. Statement-I: int (dx)/(sqrt(9 -x^(2))) = sin^(-1) ((x)/(3)) + c Statem...

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  5. S(1) : int (x^(5))/(x^(2) + 1) dx = (x^(4))/(4) - (x^(2))/(4) - (x^(2)...

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  6. If the curve f(x) = int e^(x) dx passing through (0,1) then the ascend...

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  7. If int (1)/(sqrt(x^(2) + x+ 1)) dx = a sinh^(-1) (bx + c ) + d then ...

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  8. If int (dx)/(cos^(3) x sqrt(2 sin 2x)) = (tan x)^(A) + C(tan x)^(B) + ...

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  9. Observe the following statements Assertion (A) : int((x^(2) -1)/(x^(...

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  10. Assertion (A) : int (2 x tan x sec^(2) x + tan^(2) x) dx = x tan^(2)...

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  11. The anti derivativ of f(x) = 1 +2^(x) log 2 is g(x) and the curve y =...

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  12. If int (1)/(cos^(6) x + sin^(6) x) dx = tan^(-1) f(x) + C then f(x) =

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  13. int(f(x)g'(x)-f'(x)g(x))/(f(x)g(x)) [ log (g(x))-log(f(x))]dx=

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  14. If int x^(3)e^(5x)dx-(e^(5x))/(5^(4))(f(x))+0(3) then f(x)=

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  15. int (x)/((x^(2)+2x+2)^(2))dx=

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  16. If int log (a^(2)+x^(2))dx=h(x)+c, then h(x)=

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  17. For x gt 0, if int(logx)^(5)dx=x(A(logx)^(5)+B(logx)^(4)+C(logx)^(3)+D...

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  18. int (3 sinx - 5 cos x )/(7 cos x + 2 sin x ) dx =

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  19. int (1 - x^(7))/(x (1 + x^(7)))" dx = a l n" |x| + bln |x^(7) + 1 |+ c...

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  20. int (6x^(2) - 17 x - 5)/((x - 3)(x - 2)^(2)) dx =

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