作业帮求一下几个积分,高数大一∫[1/(1-x-a)]dx∫(10^-y)dy∫(1/sinx)dx∫[(-10^-y)/ln10]dy
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求一下几个积分,高数大一∫[1/(1-x-a)]dx∫(10^-y)dy∫(1/sinx)dx∫[(-10^-y)/ln10]dy
求一下几个积分,高数大一
∫[1/(1-x-a)]dx
∫(10^-y)dy
∫(1/sinx)dx
∫[(-10^-y)/ln10]dy
求一下几个积分,高数大一∫[1/(1-x-a)]dx∫(10^-y)dy∫(1/sinx)dx∫[(-10^-y)/ln10]dy
∫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
∫[1/﹙1-x-a﹚]dx=-ln|1-x-a|+c
∫﹙10^-y﹚dy=(10^-y/㏑10﹚+c
∫(1/sinx)dx=㏑| cscx-cotx |+c
∫[(-10^-y)/ln10]dy =-10^-y+c
其中c为任意常数