Question

求不定积分1/(2^x+5^x)dx 明天考试了，各位大佬帮帮忙啊，谢谢了

求不定积分1/(2^x+5^x)dx

Answer 1

1/(x^2+2x+5)dx
=∫1/[(x+1)^2+4]dx
=∫(1/4)/[ [(x+1)/2]^2+1]dx
=∫(1/4)·2/[ [(x+1)/2]^2+1]d( (x+1)/2)
=(1/2)∫1/[ [(x+1)/2]^2+1]d( (x+1)/2)
=(1/2)arctan[(x+1)/2]+ C

Answer 2

拍题目图片

追问

没有找到题目😥

追答

我不觉得这个能找到确定的原函数 所以怀疑你题目记错了 坐等打脸

追问

唉╯﹏╰好吧

Answer 3

。。。。。

Answer 4

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