** Final answer to the problem

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** 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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Combining like terms $\left(x+1\right)^2$ and $\left(x+1\right)^2$

Learn how to solve definite integrals problems step by step online.

$\int_{0}^{1}2\left(x+1\right)^2dx$

Learn how to solve definite integrals problems step by step online. Integrate the function (x+1)^2+(x+1)^2 from 0 to 1. Combining like terms \left(x+1\right)^2 and \left(x+1\right)^2. The integral of a constant times a function is equal to the constant multiplied by the integral of the function. Apply the formula: \int\left(x+a\right)^ndx=\frac{\left(x+a\right)^{\left(n+1\right)}}{n+1}+C, where a=1 and n=2. Simplify the expression.

** Final answer to the problem

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