ä¸è½å
¬å¼ â«R(sinx, cosx)dx
= â«R[2u/(1+u^2), (1-u^2)/(1+u^2)]2du/(1+u^2)
åå¹å
¬å¼
â«f(x^n)x^(n-1)dx = (1/n)â«f(x^n)dx^n
â«[f(x^n)/x]dx = (1/n)â«[f(x^n)/x^n]dx^n
â«(asinx+bcosx)dx/(psinx+qcosx)åï¼
设 asinx+bcosx = A(psinx+qcosx) + B(psinx+qcosx)'
éå¹éæ¨å
¬å¼
I<n> = â«(tanx)^ndx = (tanx)^(n-1)/(n-1) - I<n-2>
I<n> = â«(sinx)^ndx = -cosx(sinx)^(n-1)/n + (n-1)I<n-2>/n
I<n> = â«(cosx)^ndx = sinx(cosx)^(n-1)/n + (n-1)I<n-2>/n
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