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The value of int e^sqrtx/sqrtx(sqrtx + x...

The value of `int e^sqrtx/sqrtx(sqrtx + x) dx` is equal to

A

`2e^(sqrt(x))-x+1]+C`

B

`2e^(sqrt(x))[x-2sqrt(x)+1)]+C`

C

`2e^sqrt(x)[x-sqrt(x)+1]+C`

D

`2e^sqrt(x)(x+sqrt(x)+1)+C`

Text Solution

Verified by Experts

The correct Answer is:
c
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Knowledge Check

  • intsqrtx e^(sqrtx)dx is equal to

    A
    `2sqrtx-e^(sqrtx)-4sqrt(xe^(sqrtx))+C`
    B
    `(2x-4sqrtx+4)e^(sqrtx)+C`
    C
    `(2x+4sqrtx+4)e^(sqrtx)+C`
    D
    `(1-4sqrtx)e^(sqrtx)+C`
  • int sqrtx e^(sqrtx) dx is equal to

    A
    `2sqrtx-e^sqrtx +4sqrt(xe^sqrtx)+C`
    B
    `(2x-4sqrtx+4)e^sqrtx+C`
    C
    `(2x+4sqrtx+4)e^sqrt4 +C`
    D
    `(1+4sqrtx)e^sqrtx+C`
  • The value of int(e^(sqrtx))/(sqrtx(1+e^(2sqrtx)))dx is equal to (where, C is the constant of integration)

    A
    `tan^(-1)(2e^(sqrtx))+C`
    B
    `ln((1+e^(x))/(1-e^(sqrtx)))+C`
    C
    `2tan^(-1)(e^(sqrtx))+C`
    D
    `(tan^(-1)x)e^(sqrtx)+C`
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