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(1) int sqrtx/(sqrt(2x+3))dx (2) int (a...

`(1) int sqrtx/(sqrt(2x+3))dx` `(2) int (arctanx) dx`

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Knowledge Check

  • int(sqrtx+1/sqrtx)^2 dx=

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

  • int ((1+sqrtx)^2)/sqrtx dx=

    A
    `2sqrtx+4x+2/3x^5/2+c`
    B
    `sqrtx+2x+2/3x^3/2+c`
    C
    `2sqrtx+2x+2/3 x^(3//2) +c`
    D
    `3sqrtx+2x+2/3 x^(3//2) +c`

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    (i) int(x^(2) - 1/(x^(2)))^(3) dx , (ii) int(sqrt(x) -1/(sqrt(x))) dx (iii) int(sqrt(x) + 1/(sqrt(x)))^(2) dx , (iv) int((1+2x)^(3))/(x^(4)) (v) int((1+x)^(3))/(sqrt(x)) dx , (vi) int(2x^(2)+x-2)/((x-2)) dx

    int(sqrt(x) - 1/(sqrtx))^(2) dx .

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

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