how do you do this separable equations problem: dx/dt = te^t x(0)=1

how do you do this separable equations problem: dx/dt = te^t x(0)=1

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\[\frac{dx}{dt}=te^t \rightarrow dx=te^tdt \rightarrow \int\limits_{}{}dx=\int\limits_{}{}te^tdt\]

\[\frac{dx}{dt}=te^t \rightarrow dx=te^tdt \rightarrow \int\limits_{}{}dx=\int\limits_{}{}te^tdt\]

This is just\[x=e^t(t-1)+c\]

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