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The integral (sin^(2)xcos^(2)x)/((sin^(5...

The integral `(sin^(2)xcos^(2)x)/((sin^(5)x+cos^(3)xsin^(2)x+sin^(3)xcos^(2)x+cos^(5)x)^(2))dx` is equal to

A

`(-1)/(1+cot^(3)x)+C`

B

`(1)/(3(1+tan^(3)x))+C`

C

`(-1)/(3(1+tan^(3)x))+C`

D

`(1)/(1+cot^(3)x)+C`

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • int(sin^(6)x+cos^(6)x+3sin^(2)xcos^(2)x)dx is equal to

    A
    `x+C`
    B
    `(3)/(2)sin2x+C`
    C
    `-(3)/(2)cos2x+C`
    D
    `(1)/(3)sin3x-cos3x+C`

  • int(cos x + x sin x)/(x^(2) + x cos x)dx is equal to

    A
    `log|(sin x)/(1+cos x)| + c`
    B
    `log |(sin x)/(x + cos x)| + c`
    C
    `log |(2 sin x)/(x+cos x)|+c`
    D
    `log|(x)/(x+cos x)|+c`

  • The integral int(sin2x(1-(3)/(2)cosx)dx)/(e^(sin^(2)x+cos^(3)x))= a) e^(sin^(2)x+cos^(3)x)+C b) -e^(-(sin^(2)x+cos^(3)x))+C c) e^(-(sin^(2)x+cos^(3)x)^(2))+C d)None of these

    A
    `e^(sin^(2)x+cos^(3)x)+C`
    B
    `-e^(-(sin^(2)x+cos^(3)x))+C`
    C
    `e^(-(sin^(2)x+cos^(3)x)^(2))+C`
    D
    None of these

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