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Evaluate: int(x^3)/(x+1)dx...

Evaluate: `int(x^3)/(x+1)dx`

Text Solution

Verified by Experts

The correct Answer is:
`(x^(3))/(3)+x-(x^(2))/(2)-" In "|x+1|+C`
`x^(3)/(x+1)=(x^(3)+1-1)/(x+1)=(-1)/((x+1))+(x^(2)+1-x)`
Thus, the given integral is
`int(x^(2)+1-x-(1)/(1+x))dx=(x^(3))/(3)+x-(x^(2))/(2)-" In "|x+1|+C`
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