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问题：不定积分∫（3^x*5^x/25^x-9^x）dx
答案：↓↓↓ 钱素琴的回答： 网友采纳 ∫3^x×5^x/(25^x-9^x)dx =∫3^x×5^x/[(5²)^x-(3²)^x]dx =∫[1/(5^x-3^x)-1/(5^x+3^x)]×5^xdx =∫{1/[(5/3)^x-1]-1/[(5/3)^x+1]}×(5/3)^xdx =∫{1/[(5/3)^x-1]-1/[(5/3)^x+1]}×d(5/3)^x/ln(5/3) =[1/ln(5/3)]×[ln|(5/3)^x-1|-ln|(5/3)^x+1|+C =[1/ln(5/3)]×ln|[(5/3)^x-1]/[(5/3)^x+1]|+C =[1/ln(5/3)]×ln|(5^x-3^x)/(5^x+3^x]|+C | 
