Complex numbers use to solve the definite integral

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]

So,

variable.

Just at present, we need to find beneath integral:

and

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:

Reply:

Through complex numbers to work a few difficult, but mean this method helps to solve other integrals.

References:

1. G. N. Berman. “Problems of mathematical analysis”. Moscow 1985.
2. Yo.U.Soatov. “Higher mathematics” part-2. Tashkent. “Teacher” 1994.