Evaluate:
$$\int_{0}^{1} \frac{dx}{1 + x^3}$$
The bounds are not from 0 to infinity or from -infinity to infinity etc..
How can we use complex contour integration for this? Thanks
2026-04-04 07:50:22.1775289022
Complex Contour Integrals from integrals from $0 \to 1$
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You could transform the bounds:
$$\int_0^1 \frac{\text{d}x}{1+x^3} \stackrel{\left( x= \frac{1}{t+1}\right)}{=} \int_{0}^{+\infty} \frac{t+1}{(t+1)^3+1}\text{d}t$$
I haven't checked if the latter one is solvable using complex contor integration. But I dont see any reason why it wouldn't.