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For x^2nenpi+1, n inN(the set of natural...

For `x^2nenpi+1, n inN`(the set of natural numbers), the integral `intxsqrt((2sin(x^2-1)-sin2(x^2-1))/(2sin(x^2-1)+sin2(x^2-1)))`dx is equal to (where c is a constant of integration)

A

`log |1/2 sec(x^(2)+1)|+C`

B

`log|sec((x^(2)+1)/(2))|+C`

C

`1/2 log |sec(x^(2)+1)|+C`

D

None of these

Text Solution

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The correct Answer is:
B
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ARIHANT MATHS ENGLISH-INDEFINITE INTEGRAL -Exercise (Single Option Correct Type Questions)
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  4. If n is a positive odd integer, then int |x^n| dx=

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  5. Let F(x) be the primitive of (3x+2)/(sqrt(x-9)) w.r.t. x. If F(10)=60...

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  6. int(x^x)^x(2xlogex+x)dx is equal to

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  7. The value of int x log x (log x - 1) dx is equal to

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  8. int(x^2-1)/(x^3sqrt(2x^4-2x^2+1))dx is equal to (a) (sqrt(2x^4-2x^2+1...

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  9. Let f(x) be a polynomial satisfying f(0)=2 , f'(0)=3 and f''(x)=f(x) t...

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  10. int(e^((x^(2)+4Inx))-x^(3)e^(x^(2)))/(x-1)dx equals to

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  11. int tan^(4)x dx = A tan^(3) x+ B tan x + f(x), then

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  12. If the anti derivative of int sin^4x/x dx is f(x) then int(sin^4(p+q)...

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  13. Prove that : sintheta/cos(3theta)+sin(3theta)/cos(9theta)+sin(9theta)...

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  14. For x^2nenpi+1, n inN(the set of natural numbers), the integral intxsq...

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  15. int(dx)/(cos(2x)cos(4x))=

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  16. int(1-7cos^(2)x)/(sin^(7)xcos^(2)x)dx=(f(x))/((sinx)^(7))+C, then f(x)...

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  18. The primitive of the function f(x)= x | cos x|, when pi/2 lt x lt pi i...

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  19. The primitive of the function f(x)=(2x+1)|sin x|, when pi lt x lt 2 p...

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  20. If f(x)=|(0,x^2-sinx,cosx-2),(sinx-x^2,0,1-2x),(2-cosx,2x-1,0)|,then i...

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