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Evaluate ∫ (x+2)(x 2 +1) (x 2 +x+1...

Evaluate ∫ (x+2)(x 2 +1) (x 2 +x+1) ​ dx

Text Solution

Verified by Experts

The correct Answer is:
`(x^(2))/(2)+log|x^(2)-1|+(1)/(2)"log"|(x-1)/(x+1)|+C`
`int(x^(2)+x+1)/(x^(2)-1)dx=int(x+(2x+1)/(x^(2)-1))dx`
`=int x dx+int(2x)/(x^(2)-1)dx+int(1)/(x^(2)-1)dx`
`=(x^(2))/(2)+log|x^(2)-1|+(1)/(2)"log"|(x-1)/(x+1)|+C`
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