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int(x+1)/(x(1+x e^x))dx...

`int(x+1)/(x(1+x e^x))dx`

A

`log|1+xe^(x)|+x+C`

B

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

C

`log|(xe^(x))/(1+xe^(x))|+C`

D

`log|((x+1)e^(x))/(1+xe^(x))+C`

Text Solution

Verified by Experts

The correct Answer is:
C
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MCGROW HILL PUBLICATION-INDEFINITE INTEGRATION-EXERCISE (LEVEL 1 (SINGLE CORRECT ANSWER TYPE QUESTION ))
  1. int3^(3^(3^(x)))3^(3^(x))3^(x)dx is equal to

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  2. The value of int log (1-sqrt(x)) dx is

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  3. int(x+1)/(x(1+x e^x))dx

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  4. lf int ( sin 2x- cos 2 x) dx=1/(sqrt(2))sin (2x-a) + C, then a=

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  5. int(x+sinx)/(1-cosx)dx=

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  6. int(sin2x)/(sin^4x+cos^4x)d x

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  7. The function f whose graph passes through (pi//4, 0) and whose derivat...

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  8. The function f whose graph passes through (4, - 20) and whose derivati...

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  9. If it is know that at the point x = 1 two anti- derivatives of ...

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  10. If int(dx)/(cos^(6)x+sin^(6)x)=tan^(-1)(-Kcot2x)+C then

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  11. If int(sin^(2)x)/(1+sin^(2)x)dx=x-Ktan^(-1)(Mtanx)+C then

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

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  13. If int log(sqrt(1-x)+sqrt(1+x))dx=xf(x)+Ax+Bsin^(-1)x+C, then

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  14. I fintxlog(1+1/ x)dx=f(x)log(x+1)+g(x)x^2+dx+C ,t h e n

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  15. If int(1)/((x^(2)+1)(x^(2)+4))dx=Atan^(-1)x+B" tan"^(-1)(x)/(2)+C , t...

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  16. If int(cos^(4)x)/(sin^(4)x)dx=Kcotx+Msin2x+L(x)/(2) + C then

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  17. If int(xe^(x))/(sqrt(1+e^(x)))dx=f(x)sqrt(1+e^(x))-2logg(x)+C, then

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

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  19. If int cosec 2x dx = f|g(x)| + C then

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  20. If int f(x) dx = 2 cos sqrt(x) + c, then f(x) =

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