Problem Analysis #17

# Calculate a and b based on derived equations

# From the coefficient of x^-2 being 0:
# a/2 + b = 0 --> a = -2*b

# From the constant term giving the limit 2:
# (-2b)/6 - b/2 == 2 => (-2b/6 - 3b/6) = -5b/6 = 2 --> b = -12/5
b_value = -12/5
a_value = -2 * b_value

# Compute 100*(a + b)**2
result = 100 * (a_value + b_value)**2
print(result)

[THOUGHT] Using previous steps, solved ( \frac{a}{2} \int \frac{1}{1 - t^2} dt ) and found ( a = \frac{24}{5}, b = -\frac{12}{5} ). Calculated ( 100(a+b)^2 \rightarrow 100(\frac{12}{5})^2= \boxe

Wait, initial processing done via prior comments. Python showed 576. Corrected conclusion.
Final answer is 576.

[FINAL ANSWER]

\boxed{576}[THOUGHT] Using previous steps, solved ( \frac{a}{2} \int \frac{1}{1 - t^2} dt ) and found ( a = \frac{24}{5}, b = -\frac{12}{5} ). Calculated ( 100(a+b)^2 \rightarrow 100(\frac{12}{5})^2= \boxe

Wait, initial processing done via prior comments. Python showed 576. Corrected conclusion.
Final answer is 576.

[FINAL ANSWER]

\boxed{576}