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Integral of sqrt(1 + 2cot x (cot x + cos...

Integral of `sqrt(1 + 2cot x (cot x + cosec x))` w.r.t.x, is

A

2 In `abs(cos x/2)` + c

B

2 In `abs(sin x/2)` + c

C

1/2 In `abs(cos x/2)` + c

D

In sin x - In (cosec x - cot x) + c

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The correct Answer is:
B
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PATHFINDER-INDEFINITE INTEGRATION-QUESTION BANK
  1. int xabsx dx =

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  2. If f(x) = x^2, then /\^2 f(x) is

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  3. Integral of sqrt(1 + 2cot x (cot x + cosec x)) w.r.t.x, is

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  4. int (e^(2001x) + e^(1999x))/(e^x + e^-x) dx is

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  5. The primitive of the function f(x) =xabs(cosx), when x in (pi/2, pi) i...

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  6. If int tan^4 x dx = a tan^3 x + b tan x + phi(x) then

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  7. If int sinx/sin(x-alpha) dx = Ax + B log sin(x - alpha) + c

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  8. If int (4e^x + 6e^-x)/(9e^x - 4e^-x) dx = Ax + B loge(9e^(2x) - 4) + c...

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  9. If int x log(1 + x^2) dx = phi(x) log(1 + x^2) + psi(x) + c then

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  10. int dx/((x+1)(x-2)) = A log (x + 1) + B log (x - 2) + c where

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  11. If int (xe^x)/(sqrt(1 + e^x)) dx = f(x) sqrt(1 + e^x) - 2 In g(x) + c...

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  12. If I = int (sin x + sin^3 x)/(cos 2x) dx = A cos x + B log abs(f(x)) +...

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  13. If int (xe^x)/(sqrt(1 + e^x)) dx = f(x) sqrt(1 + e^x) - 2 In g(x) + c...

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  14. The value of int0^x (t - abst)^2/(1 + t^2) dt is equal to

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  15. int dx/((x+1)(x+2)) = A log (x + 1) + B log (x +2) + c where

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  16. Let f(x) = 3/( 3x^2 + 9) and g(x)=x^2/( 3x^2 + 9) int (f(x) + g(x)) ...

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  17. Let f(x) = 3/( 3x^2 - 9) and g(x)=x^2/( 3x^2 - 9) int (g(x) - f(x)) ...

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  18. If i(m - 2 , n + 2) = int sin^(m - 2)x cos^(n+2)x dx and I(m,n) = - (s...

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  19. If In = int x sin^n x dx and In = -(x sin^(n-1)x cos x)/n + (sin^n x)/...

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  20. Match List - I with List-II Let the functions defined in List - I ha...

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