Question Number 52988 by Joel578 last updated on 16/Jan/19
$$\int\:\frac{{x}^{\mathrm{2}} }{\:\sqrt{\mathrm{1}\:+\:{x}^{\mathrm{4}} }}\:{dx} \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 16/Jan/19
$$\int{x}^{\mathrm{2}} ×\left(\mathrm{1}+{x}^{\mathrm{4}} \right)^{\frac{−\mathrm{1}}{\mathrm{2}}} {dx} \\ $$$$\int{x}^{\mathrm{2}} \left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}{x}^{\mathrm{4}} +\frac{\mathrm{1}×\mathrm{3}}{\mathrm{2}×\mathrm{4}}{x}^{\mathrm{8}} −\frac{\mathrm{1}×\mathrm{3}×\mathrm{5}}{\mathrm{2}×\mathrm{4}×\mathrm{6}}{x}^{\mathrm{12}} +…\right){dx} \\ $$$$\int\left({x}^{\mathrm{2}} −\frac{\mathrm{1}}{\mathrm{2}}{x}^{\mathrm{6}} +\frac{\mathrm{1}×\mathrm{3}}{\mathrm{2}×\mathrm{4}}{x}^{\mathrm{10}} −\frac{\mathrm{1}×\mathrm{3}×\mathrm{5}}{\mathrm{2}×\mathrm{4}×\mathrm{6}}{x}^{\mathrm{14}} +…\right){dx} \\ $$$$=\frac{{x}^{\mathrm{3}} }{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{2}}×\frac{{x}^{\mathrm{7}} }{\mathrm{7}}+\frac{\mathrm{1}×\mathrm{3}}{\mathrm{2}×\mathrm{4}}×\frac{{x}^{\mathrm{11}} }{\mathrm{11}}−\frac{\mathrm{1}×\mathrm{3}×\mathrm{5}}{\mathrm{2}×\mathrm{4}×\mathrm{6}}×\frac{{x}^{\mathrm{15}} }{\mathrm{15}}…+{c} \\ $$$${i}\:{can}\:{not}\:{solve}\:{using}\:{others}\:{way}\:{hence}… \\ $$