Question

∫dx /(9+25x^2)

Answer 1

∫dx /(9+25x^2)

=(1/9)*∫dx/[1+(5x/3)^2]

=(1/9)*(3/5)∫d(5x/3)/[1+(5x/3)^2]

=(1/15)*∫du/(1+u^2)

=（1/15）*arctan(u)+c

=(1/15)*arctan(5x/3)+c

注意：∫du/(1+u^2)

=∫d(tanA)/[1+(tanA)^2]

=∫[(secA)^2/(secA)^2]*dA

=A+c

=arctan(u)+c