Find all the antiderivatives of the following function. Check your work by taking the derivative.
f(x)=10 e^x

[tex] \int 10e^x dx = 10 \int e^x dx = 10 e^x + C [/tex]

The first step, factoring out the constant 10, is due to the Constant Multiple Rule:

[tex] \int k \cdot f(x) dx = k \cdot \int f(x) dx [/tex]

The derivative of the natural exponential function is itself! [tex] \frac{d}{dx} \left( e^x \right) = e^x [/tex]. Reversing this,

[tex] \int e^x dx = e^x + C [/tex]