Yet Another Easy Calculus Problem!?

Question

Find the antiderivative of f(x) = -x^2 - e^(-x)

Please show all work!

Answer 1

Let Int{ } be the sign of integral of a given function.

The antiderivative of a given function is equal to find the undefined integral of it.

Int{ -x² - exp(-x)}dx

First, we can separate the sum:

Int{-x² - exp(-x))dx = Int{-x²dx} - Int{exp(-x)dx}

We solve the first integral:

Int{-x²dx} = - Int{x²dx} = -x³/3 +C1

We solve the second integral:

Int{exp(-x)dx} = -exp(-x) + C2

We just have to add both results:

-x³/3 + exp(-x) + C............(both C1 and C2 can be combined in just a single constant)

That´s it!

Good luck!

Answer 2

F(x)=-x^3 /3 +e^{-x} +C