What is the antiderivative of $3e^x$ ?

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Answer 1 · 2016-01-27T15:42:31

$3e^x+C$

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 $inte^udu=e^u+C$

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

What is the antiderivative of 3e^x3e^x?