帮忙求一下不定积分(2的x次方+1/3的x次方+e的x次方/5)dx急!

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/05 19:46:31
帮忙求一下不定积分(2的x次方+1/3的x次方+e的x次方/5)dx急!

帮忙求一下不定积分(2的x次方+1/3的x次方+e的x次方/5)dx急!
帮忙求一下不定积分(2的x次方+1/3的x次方+e的x次方/5)dx急!

帮忙求一下不定积分(2的x次方+1/3的x次方+e的x次方/5)dx急!
∫[2^x+(1/3)^x+e^x/5]dx
=∫2^xdx+∫(1/3)^xdx+∫e^x/5dx
=(1/ln2)*∫2^xln2dx+1/ln(1/3)*∫(1/3)^xln(1/3)dx+∫e^x/5dx
=2^x/ln2+(1/3)^x/ln(1/3)+e^x/5+C
=2^x/ln2-(1/3)^x/ln3+e^x/5+C