09/04/28 01:32:12
>>368
t = cos(x)とおいて
dt/dx = -sin(x)
∫{1/sin(x)} dx = ∫{ sin(x)/sin(x)^2} dx
= ∫{sin(x)/(1-cos(x)^2)} dx
= ∫{1/(t^2 -1)} dt
= (1/2)∫{ (1/(t-1)) - (1/(t+1))} dt
= (1/2) { log|t-1| - log|t+1|} +c
09/04/28 01:32:12
>>368
t = cos(x)とおいて
dt/dx = -sin(x)
∫{1/sin(x)} dx = ∫{ sin(x)/sin(x)^2} dx
= ∫{sin(x)/(1-cos(x)^2)} dx
= ∫{1/(t^2 -1)} dt
= (1/2)∫{ (1/(t-1)) - (1/(t+1))} dt
= (1/2) { log|t-1| - log|t+1|} +c