Final answer to the problem
$x+2e^{\left(3+2x\right)}+\frac{7}{4}e^{2x}-\frac{7}{2}xe^{2x}+\frac{7}{2}x^2e^{2x}-e^{2x}x^{3}+\frac{1}{2}e^{2x}x^4+C_0$
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Step-by-step Solution
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- Integrate by partial fractions
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- Integrate using tabular integration
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- Weierstrass Substitution
- Integrate using trigonometric identities
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- Product of Binomials with Common Term
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1
Simplify the expression
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$\int1dx+\int4x^2e^{2x}dx+\int4e^{\left(3+2x\right)}dx+\int x^4e^{2x}dx$
Learn how to solve problems step by step online. Find the integral int(1+4x^2e^(2x)4e^3e^(2x)x^4e^(2x))dx. Simplify the expression. The integral \int1dx results in: x. Multiply the single term 4 by each term of the polynomial \left(\frac{1}{2}x^2e^{2x}-\frac{1}{2}xe^{2x}+\frac{1}{4}e^{2x}\right). Simplifying.
Final answer to the problem
$x+2e^{\left(3+2x\right)}+\frac{7}{4}e^{2x}-\frac{7}{2}xe^{2x}+\frac{7}{2}x^2e^{2x}-e^{2x}x^{3}+\frac{1}{2}e^{2x}x^4+C_0$
