So I have the following integral. $$\int_0^{1} \frac{x^a-x^b}{\log x} \sin(\log x)\,\text{d}x. $$ I thought of a substitution like this $$\log x=t \implies (e^{a-1}-e^{b-1})\int_{-\infty}^{0}e^{-t}\frac{\sin t}{t}\,\text{d}t.$$ Is it correct? or am I missing something?
2026-03-28 05:20:40.1774675240
Integral with log and sin
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