• # question_answer $\int_{{}}^{{}}{\frac{{{x}^{8}}+4}{{{x}^{4}}-2{{x}^{2}}+2}dx,}$then which of the following is correct? A)  $\frac{{{x}^{5}}}{5}-\frac{2{{x}^{3}}}{3}+2x+C$               B)  $\frac{{{x}^{5}}}{5}-\frac{2{{x}^{3}}}{3}-2x+C$ C)  $\frac{{{x}^{5}}}{5}+\frac{2{{x}^{3}}}{3}-2x+C$               D)  $\frac{{{x}^{5}}}{5}+\frac{2{{x}^{3}}}{3}+2x+C$

We have given that $\int_{{}}^{{}}{\frac{{{x}^{8}}+4}{{{x}^{4}}-2{{x}^{2}}+2}}dx=\int_{{}}^{{}}{\frac{({{x}^{8}}+4=4{{x}^{4}})-4{{x}^{4}}}{({{x}^{4}}-2{{x}^{2}}+2)}}dx$ $=\int_{{}}^{{}}{\frac{{{({{x}^{4}}+2)}^{2}}-{{(2{{x}^{2}})}^{2}}}{({{x}^{4}}-2{{x}^{2}}+2)}}dx$ $=\int_{{}}^{{}}{\frac{({{x}^{4}}+2+2{{x}^{2}})({{x}^{4}}+2-2{{x}^{2}})}{({{x}^{4}}-2{{x}^{2}}+2)}}dx$ $=\int_{{}}^{{}}{({{x}^{4}}+2{{x}^{2}}+2)}dx$ $=\frac{{{x}^{5}}}{5}+\frac{2}{3}{{x}^{3}}+2x+C$