Question

求一下几个积分,高数大一∫[1/(1-x-a)]dx∫(10^-y)dy∫(1/sinx)dx∫[(-10^-y)/ln

Answer 1

∫dx/(1-x-a)= -∫d(1-x-a)/(1-x-a)=-ln|1-x-a|+C

∫10^(-y)dy

=∫(1/10)^ydy

=[1/ ln(1/10)] * (1/10)^y +C

∫dx/sinx=∫sinxdx/(1-cosx^2)=-∫dcosx/[(1-cosx)(1+cosx)]=-(1/2)ln|(1+cosx)/(1-cosx)|+C

=-ln|(1+cosx)/sinx|+C

=-ln|cscx+cotx|+C

∫(-10^(-y)/ln10 dy

=(-1/ln10)∫(1/10)^ydy

=(-1/ln10)*(1/ln(1/10))*(1/10)^y +C

=1/(ln10)^2 *(1/10)^y +C