Evaluate: (i) `intcos^2x3sinx\ dx` (ii) `int(e^x)/((1+e^x)^2)\ dx`

Explanation

`\text { evaluate: } \int x^{2} \sqrt{1+x} d x \text {. }`


`I=\int x^{2} \sqrt{1+x} d x`


`\text { c } u=\sqrt{x+1}`


`d u=\frac{1}{2 \sqrt{x+1}} d x .`


`\int x^{2} \cdot \sqrt{x+1} d x=2 \int(u^{2}-1)^{2} \cdot u^{2} d u=2`


`I=2 \int(u^{6}-2 u^{4}+u^{2}) d u=`


`I=2[\frac{x^{7}}{7}-\frac{24^{5}}{5}+\frac{u^{3}}{3}]`


`\text { replacing } u=\sqrt{1+x}, \text { weget }`

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