Antiderivative Determine the antiderivative of the integral (2x+5)e^(x^2+5x). Solution 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.

1. Antiderivative
Determine the antiderivative of the integral (2x+5)e^(x^2+5x).
Solution
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