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If int(dx)/(5-4cosx)=Atan^(-1)(Btanx//2...

If `int(dx)/(5-4cosx)=Atan^(-1)(Btanx//2)+C`, then

A

`A=1,B=3`

B

`A=2//3,B=3`

C

`A=-1,B=1//3`

D

`A=1//3, B=2//3`

Text Solution

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The correct Answer is:
B
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OBJECTIVE RD SHARMA-INDEFINITE INTEGRALS-Exercise
  1. int(dx)/(x(x^n+1)) is equal to

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  2. int a^(sqrtx)/sqrt(x) dx is equal to

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  3. If int(dx)/(5-4cosx)=Atan^(-1)(Btanx//2)+C, then

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  4. If I=int(dx)/(x^(4)sqrt(a^(2)+x^(2))), then I equals

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  5. The value of the integral int(log(x+1)-logx)/(x(x+1))dx is

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  6. But for all arbitrary constants, intsqrt((1+sintheta-sin^(2)theta-s...

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  7. If x^2!=n pi-1, n in N. Then, the value of int x sqrt((2sin(x^2+1)-sin...

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  8. Given f(x) =|{:(0,x^(2)-sinx,cosx-2),(sinx-x^(2),0,1-2x),(2-cosx,2x-1,...

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  9. int(1)/(x^(1//2)(1+x^(2))^(5//4))dx is equal to

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  10. int(x^(2))/((a+bx^(2))^(5//2))dx is equal to

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  11. int(sin^(3)x)/((1+cos^(2)x)sqrt(1+cos^(2)x+cos^(2)x+cos^(4))x)dx is eq...

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  12. int(1)/(sqrt(sin^(3)xsin(x+alpha)))dx is equal to

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  13. The antiderivative of (3^(x))/(sqrt(1-9^(x))) with respect to x is

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  14. Integration of (1)/(sqrt(x^(2)=9)) with respect to (x^(2)+1) is equa...

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  15. If int(sintheta-costheta)/((sintheta+costheta)sqrt(sinthetacostheta+s...

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  16. The primitive of the function f (x) =(2x+1)|cosx|, when (pi)/(2)ltxl...

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  17. The primitive of the function f (x) = (2x+1) |sinx|, where piltxlt2p...

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  18. Let intsqrt((5-x)/(2+x))dx equal

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  19. The value of the integral int(xsin x^(2)e^(secx^(2)))/(cos^(2)x^(2))dx...

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  20. int(x^(2)-1)/(xsqrt((x^(2)+alphax+1))(x^(2)+betax+1))dx is equal to

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