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Evaluate: (i) int((x^3+8)(x-1))/(x^2-2x+...

Evaluate: (i) `int((x^3+8)(x-1))/(x^2-2x+4)\ dx` (ii) `int(atanx+bcotx)^2\ dx`

Text Solution

Verified by Experts

The correct Answer is:
`x^(3)/3+x^(2)/2-2x+C`
`int((x^(3)+8)(x-1))/(x^(2)-2x+4)dx=int((x^(3)+2^(3))(x-1))/(x^(2)-2x+4)dx`
`=int((x+2)(x^(2)-2x+4)(x-1))/(x^(2)-2x+4)dx`
`=int(x+2)(x-1)dx=int(x^(2)+x-2)dx`
`=int x^(2)dx+int xdx-2int x^(0)dx`
`=x^(3)/3+x^(2)/2-2x+C`
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