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Evaluate the integerals. int cos (l...

Evaluate the integerals.
`int cos (log x) dx on (0,oo).`

A

x [ cos (log x ) + sin (log x) ] + c

B

`(x)/(2)` [ cos (log x ) - sin (log x) ] + c

C

`(log x)/(2)` [ cos x + sin x] + c

D

`(x)/(2)` [ cos (log x ) + sin (log x) ] + c

Text Solution

Verified by Experts

The correct Answer is:
D
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AAKASH SERIES-INDEFINITE INTEGRALS -EXERCISE -II
  1. int e^(-5x).cos 12 x dx =

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  2. int 3^(x) cos 5x dx =

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  3. Evaluate the integerals. int cos (log x) dx on (0,oo).

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  4. If I(n)= int(sin nx)/(cos x)dx, then I(n)=

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  5. If I(m.n) = int sin^(m) x cos^(n) xdx then I(5,4) =

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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