$\frac{d}{dx}\left(\ln\left(\sqrt[5]{x}\left(x^2-4\right)^7e^x\right)\right)=\frac{\frac{\left(x^2-4\right)^7e^x}{5\sqrt[5]{x^{4}}}+14\sqrt[5]{x^{6}}\left(x^2-4\right)^{6}e^x+\sqrt[5]{x}\left(x^2-4\right)^7e^x}{\sqrt[5]{x}\left(x^2-4\right)^7e^x}$
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Integral
$\int\ln\left(\sqrt[5]{x}\left(x^2-4\right)^7e^x\right)dx=-\frac{71}{5}x+\frac{1}{5}x\ln\left(x\right)+14\ln\left(x+2\right)-14\ln\left(x-2\right)+7x\ln\left(x^2-4\right)+\frac{1}{2}x^2+C_0$
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