(2^x乘以3^x)/(9^X+4^X)的不定积分

Question

(2^x乘以3^x)/(9^X+4^X)的不定积分

Answer 1

(2^x乘以3^x)/(9^X+4^X)的不定积分 (分子分母同除以9^x)
=∫(2/3)^x/(1+[(2/3)^x]²)dx
=ln3/2*∫1/(1+[(2/3)^x]²)*d(2/3)^x
=ln3/2*arctan(2/3)^x+c