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On some generalization of Frullani and Dirichlet formulas. (Ukrainian) Zbl 0924.26002
The authors give formulas for the calculation of the following integrals depending on parameters: $$I_{u}(\alpha,\beta)=\int_{a}^{b}[f(\alpha u(x))-f(\beta u(x))]/v(x)dx$$ and $$D_{u}(\beta)=\int\limits_{a}^{b}\sin(\beta u(x))/v(x)dx$$, where $$f$$ is a continuous function; $$u$$ is a monotonic continuously-differentiable function; $$u(a)=0, \lim_{x\to b}u(x)=+\infty, v(x)u'(x)=\gamma u(x), \gamma=\text{const}$$.
##### MSC:
 26A06 One-variable calculus 26A48 Monotonic functions, generalizations
##### Keywords:
generalization; Frullani formula; Dirichlet formula