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Evaluate: (i) int(x^2+5x+2)/(x+2) (ii)...

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

Text Solution

Verified by Experts

(i) `int(x^2+5x+2)/(x+2)`

`=int(x(x+2)+3(x+2)-4)/(x+2)\dx`

`=int(x(x+2))/(x+2)\dx+int3dx-int(4)/(x+2)\dx`

`=intx\dx+3x-4ln(x+2)+C`

`=(x^2)/(2)+3x-4ln(x+2)+C`


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

Let, `x-2=t`

`dx=dt`

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