These article composite integrals to account we can use at complex numbers. It helps to solve voluntary composite kind of integrals. Complex numbers advantage for technics branches: electric energetic, geology, engineering geology and others.
Keywords: integral, complex number, binomial differential, function
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At this article, we say about to solve nonspecific integral at the method of complex number.
According to binomial differential:
, . [1, p 93]
In this place,
Just at present, we need to find beneath integral:
So, advantage above:
We have found of -1 complex roots: [2, p 186]
These roots of equation equal below:
, , , .
It means that at ,
Below we have found from this formula:
is odd function. So
We use from this formula as a result of:
So, we do to exchange, that is:
If we put in border:
Through complex numbers to work a few difficult, but mean this method helps to solve other integrals.
- G. N. Berman. “Problems of mathematical analysis”. Moscow 1985.
- Yo.U.Soatov. “Higher mathematics” part-2. Tashkent. “Teacher” 1994.