∫(2x3^x-5x2^x)/3^x dx
问题描述：
∫(2x3^x-5x2^x)/3^x dx
答
∫(2x3^x-5x2^x)/3^xdx=∫2xdx-∫5x(2/3)^xdx=x²-5∫xe^[xln(2/3)]dx=x²-5[x/ln(2/3)-1/ln²(2/3)]e^[xln(2/3)]+C (应用分部积分法,C是积分常数)=x²-5[x/ln(2/3)-1/ln²(2/3)](2/3)^x+C....