Question

Find all the antiderivatives of the following function. Check your work by taking the derivative.

Answer 1

$\int 10e^x dx = 10 \int e^x dx = 10 e^x + C$

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

$\int k \cdot f(x) dx = k \cdot \int f(x) dx$

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

$\int e^x dx = e^x + C$