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int (dx)/((1+sqrtx)^(8))=-(1)/(3(1+sqrtx...

`int (dx)/((1+sqrtx)^(8))=-(1)/(3(1+sqrtx)^(k_(2)))+ (2)/(7(1+sqrtx)^(k_(2)))+C,` then:

A

`K_(1)=5`

B

`k _(1)=6`

C

`k _(2)=7`

D

`k _(2)=8`

Text Solution

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The correct Answer is:
B, C
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Knowledge Check

  • int(1)/(1+sqrtx)dx=

    A
    `sqrtx-log(1+sqrtx)+c`
    B
    `2sqrtx-2log(1+sqrtx)+c`
    C
    `3sqrtx-3log(1+sqrtx)+c`
    D
    `2sqrtx+log(sqrtx-1)+c`

  • int(1)/(sqrtx+x)dx=

    A
    `log((sqrtx)/(1+sqrtx))`
    B
    `log(1+sqrtx)+c`
    C
    `2log(1+sqrtx)`
    D
    `(2)/(3)x^(3//2)-(x^(2))/(2)+c`

  • int(1)/(sqrt(1+sqrtx))dx=

    A
    `(4)/(3)(x-2)sqrt(1+x)+c`
    B
    `(4)/(3)(sqrtx-2)(1+sqrtx)+c`
    C
    `(4)/(3)(sqrt(1+sqrtx))^(3)-4sqrt(1+sqrtx)+c`
    D
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