(adsbygoogle = window.adsbygoogle || []).push({}); Antiderivative of this? - kinematics

a kinematics question

v = 1 + e^x

find x in terms of t given that x = 0 when t = 0

what i did:

dx/dt = 1 + e^x

dt/dx = 1/ (1+ e^x)

so t = the antiderivative of 1/(1+ e^x)

i tried and i kinda did this....

loge(1 + e^x)/e^x + c

but it doesnt seem right

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# Antiderivative of this?

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