Final answer to the problem
Step-by-step Solution
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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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The integral of a function times a constant ($2$) is equal to the constant times the integral of the function
Learn how to solve definite integrals problems step by step online.
$2\int x^2e^{2x}dx$
Learn how to solve definite integrals problems step by step online. Find the integral int(2x^2e^(2x))dx. The integral of a function times a constant (2) is equal to the constant times the integral of the function. We can solve the integral \int x^2e^{2x}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^{2x} a total of 3 times.
