Question Number 66044 by rajesh4661kumar@gmail.com last updated on 08/Aug/19
Answered by Tanmay chaudhury last updated on 08/Aug/19
$$\int\frac{{dx}}{{x}^{\mathrm{5}} \left(\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{4}} }\right)^{\frac{\mathrm{3}}{\mathrm{4}}} } \\ $$$${t}=\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{4}} }\rightarrow{dt}=\frac{−\mathrm{4}}{{x}^{\mathrm{5}} }{dx} \\ $$$$\int\frac{{dt}}{−\mathrm{4}×{t}^{\frac{\mathrm{3}}{\mathrm{4}}} } \\ $$$$\frac{−\mathrm{1}}{\mathrm{4}}×\frac{{t}^{\frac{−\mathrm{3}}{\mathrm{4}}+\mathrm{1}} }{\frac{−\mathrm{3}}{\mathrm{4}}+\mathrm{1}}+{c} \\ $$$$\left(−\mathrm{1}\right)\left(\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{4}} }\right)^{\frac{\mathrm{1}}{\mathrm{4}}} +{c} \\ $$