# Q.`int` `e^{log(sin x)}` `dx` is equal to = ? A) `sin x + c` B) `-cos x + c` C) `e^{log(cos x)} + c` D) None of these

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We will answer this question in different way.

`A `

`d/(dx)(sinx)=cos(x)`

so A is not possible

B `d/(dx) (-cos(x))=sin(x)`

B is not possible.

C. `d/(dx)(e^(log (cos(x))))=e^(log(cos(x)))(1/cos(x))(-sin(x))`

Thus C is not possible.

**So correct answer to your question is D.**