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int " cosec"^(3) " x dx "...

`int " cosec"^(3) " x dx "`

Text Solution

Verified by Experts

The correct Answer is:
`-(1)/(2) " cosec x cot x"+(1)/(2) log | tan.(x)/(2)|+c`
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Knowledge Check

  • The integral int sec^(2//3) "x cosec"^(4//3)"x dx" is equal to (here C is a constant of integration)

    A
    `3tan^(-1//3)x+C`
    B
    `-3tan^(-1//3)x+C`
    C
    `-3cot^(-1//3)x+C`
    D
    `-(3)/(4)tan^(-4//3)x+C`

  • int"cosec"^(4)x dx is equal to

    A
    `cotx+(cot^(3))/(3)+C`
    B
    `tanx+(tan^(3)x)/(3)+C`
    C
    `-cotx-(cot^(3)x)/(3)+C`
    D
    `-tanx-(tan^(3)x)/(3)+C`

  • The integral int_(pi//6)^(pi//3)sec^(2//3)x " cosec"^(4//3)x dx is equal to

    A
    `3^(5//6)-3^(2//3)`
    B
    `3^(7//6)-3^(5//6)`
    C
    `3^(5//3)-3^(1//3)`
    D
    `3^(4//3)-3^(1//3)`

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    int_(-pi//4)^(pi//4) "cosec"^(2) x dx

    Evaluate int "cosec"^(4)x dx

    int"cosec"^(2)(2x+5)dx

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