x→0， 1/sinx→ ∞，sinx ~ x； - 1≤sinx≤ 1， 1/sinx∈(-∞，- 1]∩[ 1，+∞)

The constant 0 is not infinitesimal.

f(x)=x？ +2x？ +x- 1=3x？ +x- 1； f'( 1)=7，f"( 1)=6

f(x)=x？ +2x？ +x- 1； f'( 1)=8，f"( 1)= 10

If f'(x)=g'(x), then f (x) = g (x)+c.

∫f(x)dx； ∫ is called an integral symbol, f(x) is called an integrand, x is called an integral variable, f(x)dx is called an integrand, and c is called an integral constant.

1.y=x？ +e^x-sinx

∫ydx=x？ /3+e^x+cosx+C

2.y=2^x+3

∫ydx=(2^x)/ln2+3x+C

3.∫lnx/xdx=∫lnxdlnx=(lnx)？ /2

4.∫xcosxdx =∫xdsinx = xsinx-∫sinxdx = xsinx+cosx+C