What is the antiderivative of 3e^x?

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##3e^x+C##

You should already understand that the derivative of ##e^x## is reasonable ##e^x##. Also, when differentiating, multiplicative firms accrue and are not altered.

Since the two components of this discharge are a multiplicative firm ##3## and ##e^x##, we can say that ##d/dx(3e^x)=3e^x##.

Thus, the antiderivative of the discharge is reasonable ##3e^x+C##.

The ##C##, or the firm of integration, is external consequently firms enjoy no appearance when judgment a derivative.

More formally, we could use adherence.

##{(u=x),((du)/dx=1=>du=dx):}##

We nonproduction to find

##int3e^xdx=3inte^xdx##

Simplify delay ##u## adherence:

##=3inte^udu##

Use the government that ##inte^udu=e^u+C##

##=3e^u+C=3e^x+C##

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