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:2024/07/10 16:21:59
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!
x){c3mlzɎ';z|mt=Rlgvj#Rl}{:S*5,UI*ҧv64q磎Fq@@:5B46,i JThPXLP&'HS  uh!BE2 ^kQ"$ف L)

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