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The value of the integral int e^(sin^2 x...

The value of the integral `int e^(sin^2 x) (cos x + cos^3 x) sin x dx` is

A

`1/2 e^(sin^2 x) (3 - sin^2 x) + c`

B

` e^(sin^2 x) (1 + 1/2 cos^2 x) + c`

C

`e^(sin^2 x) (3cos^2 x + sin^2 x) + c`

D

`e^(sin^2 x) (2 cos^2 x + 3sin^2 x) + c`

Text Solution

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The correct Answer is:
A
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PATHFINDER-INDEFINITE INTEGRATION-QUESTION BANK
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  3. The value of the integral int e^(sin^2 x) (cos x + cos^3 x) sin x dx i...

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  4. int xabsx dx =

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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