Military schools and courses of instruction in the science and art of war, / in France, Prussia, Austria, Russia, Sweden, Switzerland, Sardinia, England, and the United States. Drawn from recent official reports and documents. Revised Edition

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Equations of these surfaces in finite terms. Differential equations of the same deduced from their characteristic geometrical properties.

INTEGRAL CALCULUS.

Lessons 29–34. Integration of Functions of a Single Variable.

Object of the integral calculus. There always exists a function which has a given function for its derivative.

Indefinite integrals. Definite integrals. Notation. Integration by separation, by substitution, by parts.

Integration of rational differentials, integer or fractional, in the several cases which may present themselves. Integration of the algebraical differentials, which contain a radical of the second degree of the form √c+bx+ax². Different transformations which render the differential rational. Reduction of the radical to one of the forms

√x²+x², √a²-x², √x²-a².

Integration of the algebraical differentials which contain two radicals of the form

√a+x, √b+x,

or any number of monomials affected with fractional indices. Application to the expressions