Question

举例说明如何运用第一类换元法（凑微分法）求不定积分

Answer 1

(There is not a Chinese input program on my machine,sorry!)According to the formula ∫dx=x+C

For example

1.∫sin xdx=∫-dcosx=-cosx+C

2.∫1/x dx=∫dlnx=ln|x|+C

3.∫x^4dx=∫x^5/5dx=x^5dx+C

4.∫tanx dx=∫sinxdx/cosx=∫-dcosx/cosx

Define u=cosx ∫tan x dx=∫-du/u=-ln|u| +C

=-ln|cosx|+C