${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(t^3-2t^2+4t-3)e^{2t}dt$

Resolve this exercise with the following instructions:

evaluate integrals using integration $by$ parts, $to$ evaluate integrals using the tabulation method, $to$ evaluate trigonometric integrals containing powers $ofsine$ and cosine, $to$ evaluate trigonometric integrals containing powers $ofsecants$ and tangents, $to$ evaluate trigonometric integrals containing products $ofsine$ and cosine with different angles and $to$ solve problems using the techniques $of$ integration $by$ parts and trigonometric integrals.