不定积分∫（3^x*5^x/25^x-9^x）dx
<p>问题：不定积分∫（3^x*5^x/25^x-9^x）dx<p>答案：↓↓↓<p class="nav-title mt10" style="border-top:1px solid #ccc;padding-top: 10px;">钱素琴的回答：<div class="content-b">网友采纳 ∫3^x×5^x/(25^x-9^x)dx =∫3^x×5^x/[(5²)^x-(3²)^x]dx =∫×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) =××ln|[(5/3)^x-1]/[(5/3)^x+1]|+C =×ln|(5^x-3^x)/(5^x+3^x]|+C
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