What is the antiderivative of integrand (2x+5)e^(x^2+5x)?

To determine the antiderivative, we'll have to compute the
indefinite integral of the function f(x) =
(2x+5)*e^(x^2+5x)

Int (2x+5)*e^(x^2+5x)
dx

We notice that the exponent of e is a function whose
derivative is the other factor of the integrand.

We'll note
the exponent by t = x^2+5x and we'll solve the integral using substitution
method.

We have:

t =
x^2+5x

We'll differentiate both
sides:

dt = (x^2+5x)'dx

dt =
(2x + 5)dx

Now, we'll re-write the integral changing the
variable:

Int (2x+5)*e^(x^2+5x) dx = Int e^t
dt

 Int e^t dt = e^t + C

But t
= x^2+5x

Int (2x+5)*e^(x^2+5x) dx =
e^(x^2+5x) + C