∫t²/(t+1)dt∫x/(1-x²)dx

∫t²/(t+1)dt∫x/(1-x²)dx
∫t²/(t+1)dt
∫x/(1-x²)dx

∫t²/(t+1)dt∫x/(1-x²)dx
∫ t²/(1 + t) dt
= ∫ t(t + 1 - 1)/(1 + t) dt
= ∫ t dt - ∫ t/(1 + t) dt
= t²/2 - ∫ (t + 1 - 1)/(1 + t) dt
= t²/2 - ∫ dt + ∫ dt/(1 + t)
= t²/2 - t + ln|1 + t| + C
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∫ x/(1 - x²) dx
= ∫ d(x²/2)/(1 - x²)
= (-1/2)∫ d(1 - x²)/(1 - x²)
= (-1/2)ln|1 - x²| + C