Question

1/(√(x+9)-√x)的不定积分?

Answer 1

分母有理化

原式=∫[√(x+9)+√x]/9 dx

=1/9*(x+9)^(3/2)/(3/2)+1/9*x^(3/2)/(3/2)+C

=2(x+9)√(x+9)/27+2x√x/27+C