We present a method of integration along the lines of the Henstock-Kurzweil integral. All -derivatives are integrable in this method.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm160-1-3, author = {Paul M. Musial and Yoram Sagher}, title = {The $L^{r}$ Henstock-Kurzweil integral}, journal = {Studia Mathematica}, volume = {162}, year = {2004}, pages = {53-81}, zbl = {1063.26004}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm160-1-3} }
Paul M. Musial; Yoram Sagher. The $L^{r}$ Henstock-Kurzweil integral. Studia Mathematica, Tome 162 (2004) pp. 53-81. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm160-1-3/