求∫ （tanx / cosx ）dx
问题描述：
求∫ （tanx / cosx ）dx
答
∫sinxdx/cos^2x=-∫d(cosx)/cos^2x=-(1/2)∫d(cos^2x)/cos^3x=-(1/6)∫d(cos^3x)/cos^4x
....................n趋于无穷-(1/n)lncos^nx=0+C=C
答
原式=∫sinx/cos²x dx
=-dcosx/cos²x
=1/cosx+C
答
∫ tanx/cosx dx
= ∫ sinx/cosx * 1/cosx dx
= - ∫ d(cosx)/cos²x
= 1/cosx + C
= secx + C