Evaluate: (i) `int(cossqrt(x))/(sqrt(x))\ dx` (ii) `int(sin(tan^(-1)x)/(1+x^2)\ dx`

Explanation

(i)
`int frac{cos sqrt{x}}{sqrt{x}} d x `

`text { Let } sqrt{x}=t `

`Rightarrow frac{1}{2 sqrt{x}}=frac{d t}{d x} `

`Rightarrow frac{d x}{sqrt{x}}=2 d t `

Now, `int frac{cos sqrt{x}}{sqrt{x}} d x `

`=2 int cos t dt `

`=2 sin t+C `

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