求∫1/{(x^2+r^2)^(3/2)}dx?那位仁兄帮帮忙?

Question

求∫1/{(x^2+r^2)^(3/2)} dx?那位仁兄帮帮忙?

Answer 1

设x=r*tant,则dx=r*sec²tdt,sint=x/√(x+r)故 原式=∫r*sec²tdt/[r³sec³t]=(1/r²)∫dt/sect=(1/r²)∫costdt=(1/r²)sint+C (C是积分常数)=(1/r²)[x/√(x²+r²)]+C....