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The family of anti-derivatives of f(x)=(...

The family of anti-derivatives of `f(x)=(1)/(ax^(2)+2sqrt(ab)x+b+1)` is

A

`(1)/(2sqrt(a))log|sqrt(a)x+sqrt(b)|+C`

B

`(1)/(sqrt(a))tan^(-1)(sqrt(a)x+sqrt(b))+C`

C

`sin^(-1)(sqrt(a)x+sqrt(b))+C`

D

`e^(sqrt(a)x+sqrt(b))+C`

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Knowledge Check

  • The anti-derivative of x/(cos^(2)x) is

    A
    `xtanx+c`
    B
    `logabs(cosx)+c`
    C
    `xtanx+logabs(cosx)+c`
    D
    `cotx+c`

  • The anti-derivative of (sqrt(x) + (1)/(sqrt(x))) equals

    A
    `(1)/(3)x^(1//3) + 2x^(1//2) + C`
    B
    `(2)/(3)x^(2//3) + (1)/(2)x^(2) + C`
    C
    `(2)/(3)x^(3//2) + 2x^(1//2) + C`
    D
    `(3)/(2)x^(3//2) + (1)/(2)x^(1//2) + C`

  • The derivative of f(x) = (2 sqrt(x) - 1)/(x) is

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