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int(sqrtx)/(sqrt(x)+root(3)x)dx=...

`int(sqrtx)/(sqrt(x)+root(3)x)dx=`

A

`x-(6)/(5)root6(x^5)+(3)/(2)root3(x^2)-2sqrtx+3root3x-6root6x+6log|root6x+1|+c`

B

`x-(6)/(5)root6(x^5)+(3)/(2)root3(x^2)-2sqrtx+3root3x-6root6x-6log|root6x+1|+c`

C

`x+(6)/(5)root6(x^5)+(3)/(2)root3(x^2)+2sqrtx+3root3x-6root6x+6log|root6x+1|+c`

D

`x+(6)/(5)root6(x^5)+(3)/(2)root3(x^2)+2sqrtx+3root3x-6root6x-6log|root6x+1|+c`

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • int(sqrtx)/(1+x)dx=

    A
    `2sqrt(x)+2tan^(-1)sqrt(x)+c`
    B
    `2sqrt(x)-2tan^(-1)sqrt(x)+c`
    C
    `sqrt(x)-tan^(-1)sqrt(x)+c`
    D
    `sqrt(1+x)+c`

  • int(dx)/(4sqrtx+x)=

    A
    `2log|4+sqrt(x)|+c`
    B
    `2log|1+sqrt(x)|+c`
    C
    `(1)/(2)log|4+sqrt(x)|+c`
    D
    `(1)/(2)log|1+sqrt(x)|+c`

  • int(sqrtx)/(1+root4(x^3))dx=

    A
    `(2)/(3)(root4(x^3)-log|root4(x^3)+1|)+c`
    B
    `(2)/(3)(root4(x^3)+log|root4(x^3)+1|)+c`
    C
    `(4)/(3)(root4(x^3)-log|root4(x^3)+1|)+c`
    D
    `(4)/(3)(root4(x^3)+log|root4(x^3)+1|)+c`

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