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If I=inte^(-x)log(e^x+1)dx ,t h e nIe q ...

If `I=inte^(-x)log(e^x+1)dx ,t h e nIe q u a l` `a+(e^(-x)+1)log(e^x+1)+C` `a+(e^x+1)log(e^x+1)+C` `a-(e^(-x)+1)log(e^x+1)+C` none of these

A

`x+(e^(-x)+1)log(e^(x)+1)+C`

B

`x+(e^(x)+1)log(e^(x)+1)+C`

C

`x-(e^(-x)+1)log(e^(x)+1)+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`I=-e^(-x)log(e^(x)+1)+int(e^(-x)e^(x))/(e^(x)+1)dx `
`=-e^(-x)log(e^(x)+1)+int(e^(-x))/(e^(-x)+1)dx`
`=-e^(-x)log(e^(x)+1)-log(e^(-x)+1)+C`
`=-e^(-x)log(e^(x)+1)-log(1+e^(x))+x+C`
`=-(e^(-x)+1)log(e^(x)+1)+x+C`
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CENGAGE PUBLICATION-INDEFINITE INTEGRATION-EXERCISES (Single Correct Answer Type)
  1. If int(xln(x+sqrt(1+x^2)))/(sqrt(1+x^2))dx =asqrt(1+x^2)ln(x+sqrt(1+x...

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  2. Ifintxlog(1+1/x)dx=f(x)log(x+1)+g(x)x^2+A x+C , then f(x)=1/2x^2 (b) ...

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  3. If I=inte^(-x)log(e^x+1)dx ,t h e nIe q u a l a+(e^(-x)+1)log(e^x+1)...

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  4. Find the value of " int x sec^(2)x dx

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  5. int x sinx sec^(3)x dx is equal to

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  6. int e^(tan^(-1)x)(1+x+x^2)d(cot^(-1)x) is equal to (a) -e^(tan^(-1)x)...

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  7. inte^x((2tanx)/(1+tanx)+cot^2(x+pi/4))dx is equal to (a)e^xtan(pi/4-x...

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  8. int e^(x^4) (x^3) dx is equal to

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  9. The value of integral inte^x(1/(sqrt(1+x^2))+(1-2x^2)/(sqrt((1+x^2)^5)...

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  10. int e^x((x^2+1))/((x+1)^2)dx is equal to (a) ((x-1)/(x+1))e^x+c (b)...

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  11. int((x+2)/(x+4))^2 e^xdx is equal to

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  12. inte^(tanx)(secx-sinx)dxi se q u a lto e^(tanx)cosx+C e^(tanx)sinx...

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  13. int(cos e c^2x-2005)/(cos^(2005)x)dx is equal to (a) -(cotx)/((cosx)^...

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  14. int(1+2x^(2)+(1)/(x))e^(x^(2)-(1)/(x))dx is equal to (a) -x e^(x^(2)...

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  15. int e^(sin^(-1)x)((log(e)x)/(sqrt(1-x^(2)))+(1)/(x))dx is equal to

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  16. If xf(x)=3f^2(x)+2,t h e nint(2x^2-12 xf(x)+f(x))/((6f(x)-x)(x^2-f(x)...

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  17. The value of int(a x^2-b)/(xsqrt(c^2x^2-(a x^2+b)^2)) (a) 1/csin^(-...

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  18. int dx/((1+sqrtx)sqrt(x-x^2) is equal to ?

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  19. int(2sinx)/(3+sin2x)dx is equal to

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  20. 4int(sqrt(a^6+x^8))/x dx is equal to (a)sqrt(a^6+x^8)+(a^3)/2ln|...

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