** Final answer to the problem

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** Step-by-step Solution **

** How should I solve this problem?

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- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
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We can solve the integral $\int x^3e^{-3x}dx$ by applying the method of tabular integration by parts, which allows us to perform successive integrations by parts on integrals of the form $\int P(x)T(x) dx$. $P(x)$ is typically a polynomial function and $T(x)$ is a transcendent function such as $\sin(x)$, $\cos(x)$ and $e^x$. The first step is to choose functions $P(x)$ and $T(x)$

Learn how to solve integrals of exponential functions problems step by step online.

$\begin{matrix}P(x)=x^3 \\ T(x)=e^{-3x}\end{matrix}$

Learn how to solve integrals of exponential functions problems step by step online. Find the integral int(x^3e^(-3x))dx. We can solve the integral \int x^3e^{-3x}dx by applying the method of tabular integration by parts, which allows us to perform successive integrations by parts on integrals of the form \int P(x)T(x) dx. P(x) is typically a polynomial function and T(x) is a transcendent function such as \sin(x), \cos(x) and e^x. The first step is to choose functions P(x) and T(x). Derive P(x) until it becomes 0. Integrate T(x) as many times as we have had to derive P(x), so we must integrate e^{-3x} a total of 4 times. With the derivatives and integrals of both functions we build the following table.

** Final answer to the problem

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