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Evaluate: (i) int1/(1+sqrt(x))\ dx (ii) ...

Evaluate: (i) `int1/(1+sqrt(x))\ dx` (ii) `inte^cos^(2x)sin2x\ dx`

Text Solution

Verified by Experts

(i) `int frac{d x}{1+sqrt{x}}`
`=int frac{sqrt{x} d x}{sqrt{x}(1+sqrt{x})}`
`text { Let } 1+sqrt{x}=t`
`Rightarrow sqrt{x}=t-1`
`Rightarrow frac{1}{2 sqrt{x}}=frac{d t}{d x}`
`Rightarrow frac{d x}{sqrt{x}}=2 d t`
...
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