Final answer to the problem
$\ln\left(4x^{2}+4x^{3}+x^{4}\right)+c$
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Step-by-step Solution
How should I solve this problem?
- Choose an option
- Condense the logarithm
- Expand the logarithm
- Simplify
- Find the integral
- Find the derivative
- Write as single logarithm
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
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1
Using the power rule of logarithms: $n\log_b(a)=\log_b(a^n)$, where $n$ equals $2$
$\ln\left(\left(2x+x^2+2\right)^2\right)+c$
2
Expand the expression $\left(2x+x^2+2\right)^2$ using the square of a binomial: $(a+b)^2=a^2+2ab+b^2$
$\ln\left(4x^{2}+4x^{3}+x^{4}\right)+c$
Final answer to the problem
$\ln\left(4x^{2}+4x^{3}+x^{4}\right)+c$