Question

Determine the indefinite integral? Help needed quick!?

I=(x+8)/((x+3)(x-2))
I know to substitute u in for x-2 and set x=u+2, but then I'm left with u+10/u^2+5u and I have no idea where to go from there.

Answer 1

Step 1:

The integral is

Consider .

Decompose the equation into partial fraction.

Substitute in above expression to obtain the value of .

Equate the coefficients on each side.

Step 2:

Substitute the values of in the equation (1).

Integrate on each side.

Solution: