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

`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

Text Solution

Verified by Experts

The correct Answer is:
B
Let `=int cos^(3)e^(log sin x)dx=int cos^(3)x sin dx`
`"Put "cos x=t Rightarrow -sin xdx=dt`
`therefore I=-int t^3dt=-(t^(4))/(4)+c =-(cos^(4)x)/(4)+c`
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Knowledge Check

  • 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
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  • 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`

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    A
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    B
    `x[cos(log_ex)+sin (log_ex)]+C`
    C
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    D
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