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Evaluated : (i) intx^(7)d, (ii) intx^(...

Evaluated :
(i) `intx^(7)d`, (ii) `intx^(-7)dx` , (iii) `intx^(-1)dx`
(iv) `intx^(5//3)`, (v) `intx^(-5//4) dx` , (vi) `int2^(x) dx`
(vii) `int3sqrt(x^(2))dx` , (vii) `int(1)/(4sqrt(x^(3))) dx` , (ix) `int 2/(x^(2))dx`

Text Solution

Verified by Experts

The correct Answer is:
(i) `(x^(4))/(8) +C` , (ii) `- 1/(6x^(6)) + C` , (iii) `log |x| + C`
(iv) `3/8x^(8//3) + C` , (v) `-4x^(-1//4) + C` , (vi) `(2^(x))/(log 2) + C`
(vii) `3/5 x^(5//3) + C` , (viii) `4x^(1//4) + C` , (ix) `(-2)/(x) + C`
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intx/(3-x^(2))dx

intx/sqrt(1-x^(2))dx

Knowledge Check

  • intx^(5)/sqrt(1+x^(3))dx=

    A
    `2/3sqrt((1+x^(3))+(x^(2)+2))+c`
    B
    `2/9sqrt((1+x^(3))(x^(3)+4))+c`
    C
    `2/9sqrt(1+x^(3))(x^(3)-2)+c`
    D
    `2/9sqrt((1+x^(3))(x^(2)-2))+c`

  • intx/sqrt(x^(4)-4)dx=

    A
    `sin^(-1)(x^(2)/2)+c`
    B
    `1/2sin^(-1)(x^(2)/2)+c`
    C
    `1/2sec^(-1)(x/2)+c`
    D
    `1/2logabs(x^(2)+sqrt(x^(4)-4))+c`

  • intx/(x^(4)-1)dx=

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

    • Similar Questions

    Explore conceptually related problems

    intx^(2)/sqrt(x^(3)+1)dx

    Evaluate : (i) intx^(9)dx , (ii) int3sqrt(x) dx ,(iii) intdx (iv) int1/(x^(2))dx , (v) int(1)/(x^(1//3))dx , (vi) int5^(x) dx

    =intx^4/(sqrt(1-x^(5)))dx

    intx^5/sqrt(1+x^2)dx

    intx/sqrt(x^2+x+1)dx

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