For question #2, we use integration by partial fractions.
By multiplying each side by the denominator on the left, we get:
Expand and gather all like terms:
Equate coefficients on the right to those on the left (x^2 and x don't exist, so their coefficients must be 0):
for x^2, (A+B)=0
for x, (B+C)=0
for constant, (4A+C)=5
By solving this system, we find A=1, B=-1, C=1.
Now we can integrate (from the very first equation, plugging in A,B,C):
The first integral is easy,
The second requires us to split up the integral:
This time, the first integral is harder, we notice that this fits the formula for the derivative of arctan, with a=2:
so, the first part of this second integral is equal to:
And the second part is easy,
This leaves us with a final indefinite integral of:
Now evaluate this from 0 to 2.
This is exact. You could simplify the natural log further if you wanted to.