Question

求不定积分∫根号(9+x^2)dx

Answer 1

分部积分法：

∫√(9+x^2)dx

＝x√(9+x^2)dx－∫x^2/√(9+x^2)dx

＝x√(9+x^2)dx－∫(9+x^2-9)/√(9+x^2)dx

＝x√(9+x^2)dx－∫√(9+x^2)dx＋9∫1/√(9+x^2)dx

＝x√(9+x^2)dx－∫√(9+x^2)dx＋9ln(x+√(9+x^2))

∴∫√(9+x^2)dx＝1/2×x√(9+x^2)dx＋9/2×ln(x+√(9+x^2))＋C