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intcos^(3)xe^(log(sinx))dx is equal to...

`intcos^(3)xe^(log(sinx))dx` is equal to

A

`-(sin^(4)x)/(4)+c`

B

`-(cos^(4))/(4)+c`

C

`(e^(sin" "x))/(4)+c`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let `l=intcos^(3)x-e^(10g" sin x")dx`
`=intcos^(3)" x sin x dx"`
Put cos `x=timplies-sinxdx=dt`
`thereforel=-int t^(3)dt`
`=-(t^(4))/(4)+c`
`=-(cos^(4))/(4)+c`
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Knowledge Check

  • int cos^(3)x.e^(log(sin x)) dx is equal to

    A
    `-(sin^(4)x)/(4)+c`
    B
    `-(cos^(4)x)/(4)+c`
    C
    `-(esin^(4)x)/(4)+c`
    D
    None of these

  • int(cos^(3)x)e^(log(sinx))dx=

    A
    `-(sin^(4)x)/(4)+c`
    B
    `-(cos^(4)x)/(4)+c`
    C
    `(e^(sinx))/(4)+c`
    D
    `(sin^(4)x)/(4)+c`

  • int cos^3 xe^("log" (sin x)) dx is equal to

    A
    `- (sin^4 x)/(4) + c`
    B
    `- ("cos"^4 x)/(4) + c`
    C
    `(e^(sin x))/(4) +c `
    D
    none of these

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