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int(x^(3)-1)/(x^(3)+x)dx is equal to...

`int(x^(3)-1)/(x^(3)+x)dx` is equal to

A

`x-logx+log(x^(2)+1)-tan^(-1)x+C`

B

`x-logx+(1)/(2)log(x^(2)+1)-tan^(-1)x+C`

C

`x+logx+(1)/(2)log(x^(2)+1)+tan^(-1)x+C`

D

none of these

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The correct Answer is:
b
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OBJECTIVE RD SHARMA ENGLISH-INDEFINITE INTEGRALS-Exercise
  1. If l^(r )(x) means log log log … x, the log being repeated r times, th...

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  2. intx^(-2//3)(1+x^(1//2))^(-5//3) dx is equal to

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  3. int(x^(3)-1)/(x^(3)+x)dx is equal to

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  4. int(cosx+xsinx)/(x^(2)+xcosx)dx= . . . .

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  5. The value of int(cos2x)/(cosx) dx is equal to

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  6. int(dx)/(x(x^(n)+1)) " is equal to"

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  7. int(asqrt(x))/(sqrt(x))dx equals

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  8. If int(dx)/(5+4cosx)=Ptan^(-1)(mtanx/2)+C then,

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

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  10. int (log (x+1) - log x)/(x(x-1)) dx is equal to :

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  11. Let x^(2)ne pi-1, n in N, then intxsqrt((2sin(x^(2)+1)-sin2(x^(2)+1)...

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  12. Given, f(x)=|(0, x^(2)-sin x, cos x-2),(sin x-x^(2),0,1-2x),(2-cos x,2...

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

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

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  15. int(sin^(3)x)/((1+cos^(2)x)sqrt(1+cos^(2)x+cos^(4))x)dx is equal to

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

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

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

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

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

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