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Evaluate: (i) int(x^2+3x-1)/((x+1)^2)\ ...

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

Text Solution

Verified by Experts


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

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

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

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

Let, `x+1=t`

`dx=dt`

`=x+int(t-3)/(t^2)dt`

`=x+int((1)/(t)-(3)/(t^2))dt`

...
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