** Final answer to the problem

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** Step-by-step Solution **

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- Find the derivative using the definition
- Find the derivative using the product rule
- Find the derivative using the quotient rule
- Find the derivative using logarithmic differentiation
- Find the derivative
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x$ and $g=x^2+1$

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$\frac{d}{dx}\left(x\right)\left(x^2+1\right)+x\frac{d}{dx}\left(x^2+1\right)$

Learn how to solve problems step by step online. Find the derivative of x(x^2+1). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=x^2+1. The derivative of the linear function is equal to 1. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.

** Final answer to the problem

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