Question

(2+4u)/(2-7u-4u^2)的积分是多少?

Answer 1

(2+4u)/(2-7u-4u^2)=(2+4u)/(2+u)(1-4u)=(4/3)/(2+u)-(4/9)/(1-4u)

∫(2+4u)/(2-7u-4u^2)du

=∫(-2/3)/(2+u)du+∫(4/3)/(1-4u)du

=(-2/3)ln|2+u|-(1/3)ln|1-4u|+C