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What is the antiderivative of ##3e^x##?
##3e^x+C##
You should already know that the derivative of ##e^x## is just ##e^x##. Also, when differentiating, multiplicative constants remain and are not altered.
Since the two components of this function are a multiplicative constant ##3## and ##e^x##, we can say that ##d/dx(3e^x)=3e^x##.
Thus, the antiderivative of the function is just ##3e^x+C##.
The ##C##, or the constant of integration, is added because constants have no bearing when finding a derivative.
More formally, we could use substitution.
##{(u=x),((du)/dx=1=>du=dx):}##
We want to find
##int3e^xdx=3inte^xdx##
Simplify with ##u## substitution:
##=3inte^udu##
Use the rule that ##inte^udu=e^u+C##
##=3e^u+C=3e^x+C##