secxtanxdx=sinx/(cos^2x)dx=- 1/(cos^2x)d(cosx)=d( 1/cosx)

2. Let sinx be the original function of function f(x), then f(x)dx=(d(sinx)).

∫f(x)dx = sinx+C d∫f(x)dx = d(sinx+C)f(x)= d(sinx)

3.fˊ(x)dx=( df(x))，[f(x)dx]fˊ=(d[f(x)dx]/dx .

f'(x)dx=df(x)/dx*dx=df(x)

[f(x)dx]'=d[f(x)dx]/dx

4.(arctanx)ˇ=( 1/( 1+x^2)，(cscx)ˇ=(- 1/( 1+x^2).

5. Suppose when () is infinitesimal and when () is infinite.

6. The geometric meaning of definite integral f(x)dx is (y = the area enclosed by f (x) and x axis in the interval of [x 1, x2]).