=∫cosx/(cosx+sinx) dx

=( 1/2)∫/(cosx+sinx) dx

=( 1/2) +C

2、∫dx/( 1+cosx)

=( 1/2)∫dx/

=( 1/2)∫dx/^zhi2

=( 1/2)∫^2 dx

=tan(x/2) + C

3、∫dx/(sinx+cosx)

=∫dx/

=( 1/√2)∫csc(x+π/4) dx

=( 1/√2)ln | CSC(x+π/4)-cot(x+π/4)|+C

4 、∫(2sinx+cosx)/(sinx-cosx) dx

=( 1/2)∫/(sinx-cosx) dx

=( 1/2) + C

Algebra is a branch of mathematics, which studies the general solutions and properties of numbers, quantities, relationships, structures and algebraic equations (groups). Elementary algebra is generally taught in middle schools, introducing the basic ideas of algebra: studying what happens when we add or multiply numbers, understanding the concept of variables and how to establish polynomials and find their roots.

The research object of algebra is not only numbers, but various abstract structures. Among them, we only care about various relationships and their nature, but we don't care about the question "what is the number itself". The common types of algebraic structures are groups, rings, fields, modules, linear spaces and so on.

In ancient times, when arithmetic accumulated a large number of solutions to various quantitative problems, in order to find a systematic and more universal method to solve various quantitative relations, elementary algebra centered on the principle of solving algebraic equations was produced.

There is no doubt that algebra is developed from arithmetic. As for when algebra came into being, it's hard to say clearly. For example, you think that "algebra" refers to the skills of solving algebraic equations such as bx+k=0. This kind of "algebra" was only developed in the sixteenth century.