Final answer to the problem
Step-by-step Solution
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- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Prove from LHS (left-hand side)
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Find the derivative of $x^2$ using the definition. Apply the definition of the derivative: $\displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$. The function $f(x)$ is the function we want to differentiate, which is $x^2$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
Expand the expression $\left(x+h\right)^2$ using the square of a binomial: $(a+b)^2=a^2+2ab+b^2$
Cancel like terms $x^{2}$ and $-x^2$
Factor the polynomial $2xh+h^{2}$ by it's greatest common factor (GCF): $h$
Simplify the fraction $\frac{h\left(2x+h\right)}{h}$ by $h$
Evaluate the limit $\lim_{h\to0}\left(2x+h\right)$ by replacing all occurrences of $h$ by $0$
$x+0=x$, where $x$ is any expression