= ∫R[2u/( 1+u^2)，( 1-u^2)/( 1+u^2)]2du/( 1+u^2)

power formula

∫f(x^n)x^(n- 1)dx =( 1/n)∫f(x^n)dx^n

∫[f(x^n)/x]dx =( 1/n)∫[f(x^n)/x^n]dx^n

∫(asinx+bcosx)dx/(psinx+qcosx) type,

Let asinx+bcosx = a (psinx+qcosx)+b (psinx+qcosx)'

Reduced power recursive formula

I<n> = ∫ (tanx) ndx = (tanx) (n-1)/(n-1)-I < n-2 & gt；

I<n> = ∫ (sinx) ndx =-cosx (sinx) (n-1)/n+(n-1) I < n-2 & gt； /n

I<n> = ∫ (cosx) ndx = sinx (cosx) (n-1)/n+(n-1) I < n-2 & gt； /n