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This question is looking at integration by parts. Therefore, we need to split the integral into two parts.

Part A will be x³ and Part B will be e^x .

Draw 2 columns putt...

Firstly, let (x-2)/((x+1)(x-1)²) = A/(x+1) + B/(x-1)+C/(x-1)², where A,B and C are to be calculated. 

Then, multiply both sides of the equation by (x+1)(x-1)^2<...

Every term needs to be differentiated in terms of x:

For the x³ term, differentiated it becomes 3x² (multiply the whole term by the initial p...

So, the easiest way to start thinking about this is by looking at straight lines. The gradient of a straight line is just its slope, which is the difference in the y values between any two points...

For the x² term we add one to the power, and then divide by 3 to get x³/3 For the next term we add one to the power and divide by the new power to get 3x²/2 We do the same...