求不定积分∫1/sin^2(3x+4)dx ∫1/cos^2(6x^2+2)dx∫3ln^2x+6lnx+7/xdx∫e^x/√1-e^xdx
问题描述:
求不定积分∫1/sin^2(3x+4)dx ∫1/cos^2(6x^2+2)dx
∫3ln^2x+6lnx+7/xdx
∫e^x/√1-e^xdx
答
1.∫1/sin^2(3x+4)dx =1/3∫1/sin^2(3x+4)d(3x+4) =-1/3cot(3x+4)+C 2.∫1/cos^2(6x+2)dx =1/6∫1/cos^2(6x+2)d(6x+2) =1/6tan(6x+2)+C3.∫(3ln^2x+6lnx+7/x)dx=3xln^2(x)-6∫lnxdx+6∫lnxdx+7ln|x|+C=...