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int (log (x+1) - log x)/(x(x-1)) dx is ...

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

A

`(1)/(2)[log(x+1)]^(2)+(1)/(2)(logx)^(2)+log(x+1)logx+C`

B

`-(1)/(2)[{log(x+1)}^(2)+(logx)^(2)]+log(x+1).logx+C`

C

`(1)/(2)[log(1+1//x)]^(2)+C`

D

none of these

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Verified by Experts

The correct Answer is:
b
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int(log(x+1)-log x)/(x(x+1))dx= (A) log(x-1)log x+(1)/(2)(log x-1)^(2)-(1)/(2)(log x)^(2)+c (B) (1)/(2)(log(x+1))^(2)+(1)/(2)(log x)^(2)-log(x+1)log x+c (C) -(1)/(2)(log(x+1)^(2))-(1)/(2)(log x)^(2)+log x*log(x+1)+c (D) [log(1+(1)/(x))]^(2)+c

OBJECTIVE RD SHARMA ENGLISH-INDEFINITE INTEGRALS-Exercise
  1. If int(dx)/(5+4cosx)=Ptan^(-1)(mtanx/2)+C then,

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

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

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

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

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

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

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

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

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

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

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

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

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  15. IfI=intsqrt((5-x)/(2+x))dx ,t h e nIe q u a l sqrt(x+2)sqrt(5+x)+3si...

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

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  17. Evaluate: int(x^2-1)/(xsqrt((x^2+alphax+1)(x^2+betax+1)))dx

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  18. Evaluate int(e^(2x)-2e^(x))/(e^(2x)+1)dx

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  19. int(1)/(cosx-sinx)dx is equal to

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

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