Evaluate integral Maple

Question

I am trying to solve the following diff-equation:

$y'(t)−(3t+2)y(t) = 4e^{3t}$

I have found the solution manually and now I want to check my answer with Maple. I have defined the diff-equation:

L := D(y)(t) - (3t^2 + 2)y(t) = 4exp(3t)

Then I have found the solution:

y(t) = (Int(4exp(-t(t - 1)*(t + 1)), t) + _C1)exp(t(t^2 + 2))

Maple does not give me a reduced expression. As is seen in the result it gives an indefinite integral. How can I get maple to reduce the answer.

(I do not know how to make the commands in maple-style).

Thanks.

Answer 1

Maple does not know how to evaluate this integral.

Here value switches Int to int and then Maple tries to evaluate.
It got the integral $$ \int \frac{\exp(t)}{\exp({t^3})}\;dt $$ but it did not succeed in evaluating it, so it left it in that form.