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Evaluate: int(2x+1)/((x-1)(x+2))dx...

Evaluate: `int(2x+1)/((x-1)(x+2))dx`

Text Solution

Verified by Experts

Since all the factors in the denominator are linear, we have
`int(2x-1)/((x-1)(x+2)(x-3))dx`
`=int[(1)/((x-1)(3)(-2))+(-5)/((-3)(x+2)(-5))+(5)/((2)(5)(x-3 ))]dx`
` = -(1)/(6) log |x-1|-(1)/(3)log|x+2|+(1)/(2)log|x-3|+C`
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