几个微积分的问题,就等2天麻烦列下过程,我会追加赏分的~∫(x+1)/xdx∫x/(x+1)dx∫sec(x)dx∫arctan(x)dx∫4/(x(x-3))dx∫2/(xIn(x))dx∫In（x)dx

Question

几个微积分的问题,就等2天
麻烦列下过程,我会追加赏分的~
∫(x+1)/x dx
∫x/(x+1) dx
∫sec(x) dx
∫arctan(x) dx
∫4/(x(x-3)) dx
∫2/(xIn(x)) dx
∫In（x) dx

Answer 1

∫(x+1)/x dx= ∫(1+1/x)dx
=x+lnx+C
∫x/(x+1) dx =∫[1-1/(x+1)]dx=x-ln(x+1)+C
∫sec(x) dx =ln|secx+tanx|+C
∫arctan(x) dx =xarctanx-[ln(1+x^2)]/2+C
∫4/(x(x-3)) dx=(4/3)∫[1/(x-3)-1/x]=(4/3)*[ln(x-3)-lnx]+C
∫2/(xln(x)) dx=2∫(1/lnx)dlnx=2lnlnx+C

∫ln（x) dx=xlnx-∫dx=xlnx-x+C