Evaluate:
(i) `int((x^3+8)(x-1))/(x^2-2x+4)\ dx`
(ii) `int(atanx+bcotx)^2\ dx`

Explanation

(i) `int((x^3+8)(x-1))/(x^2-2x+4)\ dx`


`=int((x+2)(x^2-2x+4)(x-1))/(x^2-2x+4)\ dx`


`=int((x+2)(x-1)) dx`


`=int(x^2+2x-2) dx`


`=(x^3)/(3)+x^2-2x+C`



(ii) `int(atanx+bcotx)^2\ dx`


`=int(a^2tan^2x+b^2cot^2x+2ab)\dx`


`=int((a^2)(sec^2x-1)+(b^2)(cosec^2x-1)+2ab)\dx`


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