Question

For the special integral \[\int e^x\left[f(x)+f'(x)\right]dx,\] what is the antiderivative?

Options

• \[e^xf(x)+C\]

• \[e^x\left[f(x)-f'(x)\right]+C\]

• \[f(x)+f'(x)+C\]

• \[e^xf'(x)+C\]

Answer 1

The special integral has the direct result \(e^xf(x)+C\). It applies specifically when the integrand is \(e^x[f(x)+f'(x)]\).