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Evaluate: (i) int(x^2+x+5)/(3x+2)\ dx ...

Evaluate:
(i) `int(x^2+x+5)/(3x+2)\ dx`
(ii) `int(2x+3)/((x-1)^2)\ dx`

Text Solution

Verified by Experts

(i) `int(x^2+x+5)/(3x+2)\ dx`

`=int(3x^2+3x+15)/(3(3x+2))\ dx`

`=(1)/(3)int(x(3x+2))/(3x+2)dx+(1)/(3)int(x+15)/(3x+2)\ dx`

`=(x^2)/(6)+(1)/(9)int(3x+2+43)/(3x+2)\ dx`

`=(x^2)/(6)+(x)/(9)+(43ln(3x+2))/(9)+C`



(ii) `int(2x+3)/((x-1)^2)\ dx`

`=int(2(x-1)+5)/((x-1)^2)\ dx`

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