SolutionSolution by mathman · FRon peut aussi utiliser (et intégrer) la relation: ∫x+∞sin(t)tdt=cos(x)∫0+∞e−xt11+t2dt+sin(x)∫0+∞e−xtt1+t2dt\displaystyle \int_{x}^{+\infty}\frac{\sin(t)}{t}dt=\cos(x)\int_{0}^{+\infty} e^{-xt}\frac{1}{1+t^{2}}dt+\sin(x)\int_{0}^{+\infty} e^{-xt}\frac{t}{1+t^{2}}dt∫x+∞tsin(t)dt=cos(x)∫0+∞e−xt1+t21dt+sin(x)∫0+∞e−xt1+t2tdt
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