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Exercise

$\int\frac{x^3}{\sqrt{x^2+2x+5}}dx$

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Final answer to the exercise

$\frac{1}{3}\sqrt{\left(x^{2}+2x+5\right)^{3}}+5\ln\left|\sqrt{x^{2}+2x+5}+x+1\right|-\frac{3}{2}\sqrt{x^{2}+2x+5}x-\frac{5}{2}\sqrt{x^{2}+2x+5}+C_1$

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  • Integrate by partial fractions
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