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(17) If the function be (tan x)" the formula of reduction is

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CHAPTER III.

INTEGRATION OF DIFFERENTIAL FUNCTIONS OF TWO OR MORE

VARIABLES.

Sect. 1.

Functions of the first order.

In order that a differential function of two variables of the first order, such as

Pdx + Qdy, should be the differential of a function u, it is necessary that the condition

dPdQ

dy - dx should exist. When this criterion of integrability holds good, we find

u = [Pdx + sdy (Q - SPdx);

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The application of these formulæ may be generally facilitated by observing that in the second term of the former it is only necessary to integrate the terms in Q which involve x only, and in the latter those terms of P which involve y only.

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(9 Let er to the du,

Parametry: 2-5 {- #st!

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