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The value of the integral int("cosec"^(2...

The value of the integral `int("cosec"^(2)x-2019)/(cos^(2019)x)dx` is equal to (where C is the constant of integration)

A

`(cotx)/((cosx)^(2019))+C`

B

`(-cotx)/((cosx)^(2019))+C`

C

`cotx(cosx)^(2019)+C`

D

`-cotx(cosx)^(2019)+C`

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • The value of the integral inte^(x^(2)+(1)/(2))(2x^(2)-(1)/(x)+1)dx is equal to (where C is the constant of integration)

    A
    `e^(x^(2)+(1)/(x))+C`
    B
    `x^(2)(x^(2)+(1)/(x))+C`
    C
    `xe^(x^(2)+(1)/(x))+C`
    D
    `x.e^(x)+C`

  • The value of the integral I=int(2x^(9)+x^(10))/((x^(2)+x^(3))^(3))dx is equal to (where, C is the constant of integration)

    A
    `(x^(4))/(2(1+x)^(2))+C`
    B
    `(x^(6))/(2(x+1)^(2))+C`
    C
    `(x^(4))/((x+1)^(2))+C`
    D
    `(x^(6))/(2(x+1)^(3))+C`

  • Let I=int(cos^(3)x)/(1+sin^(2)x)dx , then I is equal to (where c is the constant of integration )

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

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

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