1.

Evaluate: (i) `int(sinsqrt(x))/(sqrt(x)) dx`(ii) `int((x+1)e^x)/(sin^2(x e^x)) dx`A. `-e^(x) cot x + c`B. `cos^(2) (x e^(x)) + c`C. `log sin (x e^(x)) + c`D. `- cot (x e^(x)) + c`

Answer» Correct Answer - D
Let the given integral be
`I = int (e^(x) (1 + x))/(sin^(2) (xe^(x))) dx`
Put `x e^(x) = t and e^(x) (1 + x) dx = dt`
`rArr I int (dt)/(sin^(2)t) = int "cosec"^(2) t dt`
`= - cot t + c = - cot (x e^(x)) + c`


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