Question

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

f(x)=10 e^x

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!
`(d)/(dx) \left( e^x \right) = e^x`. Reversing this,

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