Re: [微積] 一題微積分
z = tan(x/2)
dx = 2 dz /(1 + z^2)
cos x = ( 1 - z^2 ) / ( 1 + z^2 )
1 - z^2 2
=> int sqrt( 1 + -------- ) * --------- dz
1 + z^2 1 + z^2
2
= int ( ----------- )^(3/2) (z = tan y , dz = sec^2 y dy , A= 2^(3/2) )
1 + z^2
A
= int ------------ * sec^2 y dy
sec^3 y
= int A cos y dy
= A sin y + C
z
= A * -------------- + C
sqrt( z^2 + 1)
= A * tan(x/2) * cos(x/2) + C
( = 2 * sqrt( cosx + 1 ) * tan(x/2) + C )
有錯還請不吝指正。
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