Question

求下节各式的不定积分,1 ∫根号（4-x的平方）×dx 2 ∫x×e的x次方×dx 3 ∫anctan×dx 4 ∫x的

Answer 1

,1 ∫√(4-x²)dx

令x=2sint,t∈[-π/2,π/2]

∴√(4-x²)=2cost,t=arcsin(x/2)

dx=d(2sint)=2dsint=2costdt

∴ ∫√(4-x²)dx

=4ʃcos²tdt

=2ʃ(1+cos2t)dt

=2t+...