![\log_{2}^{\sqrt[3]{\frac{4.\sqrt[2]{{x}^{2} + 1}}{\sqrt[4]{x (x +2)}}}}](/latexrender/pictures/f8884ea762db836a5575e4a8cf6a2f4d.png "\log_{2}^{\sqrt[3]{\frac{4.\sqrt[2]{{x}^{2} + 1}}{\sqrt[4]{x (x +2)}}}}")
chegando até
![\frac{1}{3}. \left[\log_{2}^{4} + \log_{2}^{\sqrt[2]{{x}^{2} + 1} } - \frac{1}{4}. \left[\log_{2}^{x} + \log_{2}^{\left(x + 2 \right)} \right]\right]](/latexrender/pictures/ebfb979234a9b85518ede872ec290d91.png "\frac{1}{3}. \left[\log_{2}^{4} + \log_{2}^{\sqrt[2]{{x}^{2} + 1} } - \frac{1}{4}. \left[\log_{2}^{x} + \log_{2}^{\left(x + 2 \right)} \right]\right]")
Mas daí continuando a desenvolver o log vem a parte que eu não entendi:
![\frac{1}{3}}.\left[2 - \frac{1}{2}.\log_{2}^{\left({x}^{2} + 1 \right)} - \frac{1}{4}.\left[ \log_{2}^{x} + \log_{2}^{\left(x + 2 \right)}\right]\right]](/latexrender/pictures/0b70233e95bf43aa0deca06576858437.png "\frac{1}{3}}.\left[2 - \frac{1}{2}.\log_{2}^{\left({x}^{2} + 1 \right)} - \frac{1}{4}.\left[ \log_{2}^{x} + \log_{2}^{\left(x + 2 \right)}\right]\right]")
de onde surgui esse sinal negativo entre o número 2 e o
no livro está escrito assim mas eu não sei de onde ele vem :S.Não deveria ser:
![\frac{1}{3}}.\left[2 + \frac{1}{2}.\log_{2}^{\left({x}^{2} + 1 \right)} - \frac{1}{4}.\left[ \log_{2}^{x} + \log_{2}^{\left(x + 2 \right)}\right]\right]](/latexrender/pictures/1d0ce9bea7546d79ab54144f4f2cbc73.png "\frac{1}{3}}.\left[2 + \frac{1}{2}.\log_{2}^{\left({x}^{2} + 1 \right)} - \frac{1}{4}.\left[ \log_{2}^{x} + \log_{2}^{\left(x + 2 \right)}\right]\right]")
Por favor me ajudem, é só esse bendito sinal que está me empacando
![\frac{2}{3}+{log}_{2}\left[ \left{(x^2 + 1)}^{\frac{1}{6}}\right]-{log}_{2}\left[ \left{(x^2 + 2x)}^{\frac{1}{12}}\right]](/latexrender/pictures/73840f79a8953fcce24f03a4ce045d3b.png "\frac{2}{3}+{log}_{2}\left[ \left{(x^2 + 1)}^{\frac{1}{6}}\right]-{log}_{2}\left[ \left{(x^2 + 2x)}^{\frac{1}{12}}\right]")
![\frac{1}{3}}.\left[2 + \frac{1}{2}.\log_{2}{\left({x}^{2} + 1 \right)} - \frac{1}{4}.\left[ \log_{2}{x} + \log_{2}{\left(x + 2 \right)}\right]\right]](/latexrender/pictures/e8d9f2d7c1c6f9b676abde7de1362caa.png "\frac{1}{3}}.\left[2 + \frac{1}{2}.\log_{2}{\left({x}^{2} + 1 \right)} - \frac{1}{4}.\left[ \log_{2}{x} + \log_{2}{\left(x + 2 \right)}\right]\right]")
![\left[\frac{2}{3}+\frac{1}{6}.{log}_{2}\left(x^2 + 1\right)\right]-\frac{1}{12}.\left[{log}_{2}\left x.(x + 2)\right]](/latexrender/pictures/c22c86d2cdbdd5a745035ec25b72976a.png "\left[\frac{2}{3}+\frac{1}{6}.{log}_{2}\left(x^2 + 1\right)\right]-\frac{1}{12}.\left[{log}_{2}\left x.(x + 2)\right]")
![\frac{\sqrt[]{\sqrt[4]{8}+\sqrt[]{\sqrt[]{2}-1}}-\sqrt[]{\sqrt[4]{8}-\sqrt[]{\sqrt[]{2}-1}}}{\sqrt[]{\sqrt[4]{8}-\sqrt[]{\sqrt[]{2}+1}}}](/latexrender/pictures/981987c7bcdf9f8f498ca4605785636a.png "\frac{\sqrt[]{\sqrt[4]{8}+\sqrt[]{\sqrt[]{2}-1}}-\sqrt[]{\sqrt[4]{8}-\sqrt[]{\sqrt[]{2}-1}}}{\sqrt[]{\sqrt[4]{8}-\sqrt[]{\sqrt[]{2}+1}}}")
![\sqrt[]{2}](/latexrender/pictures/f21662d1cabab6e8b273a4b6f1cd663a.png "\sqrt[]{2}")
e elevar ao quadrado os dois lados)