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Question Number 121029 by bramlexs22 last updated on 05/Nov/20

Commented by bobhans last updated on 05/Nov/20

$$supermacho...!$$

Answered by MJS_new last updated on 05/Nov/20

$$\mathrm{super}\mathrm{easy}\mathrm{lol}!$$$$\int \frac{dx}{x^3{(x^6+1)}^{2/3}}=$$$$[t=\frac{{(x^6+1)}^{1/3}}{x^2}\to dx=-\frac{x^3{(x^6+1)}^{2/3}}{2}dt]$$$$=-\frac{1}{2}\int dt=-\frac{t}{2}=-\frac{{(x^6+1)}^{1/3}}{2x^2}+C$$

Commented by bobhans last updated on 05/Nov/20

$$haha...typowhydenomurator$$$$x^3+{(x^6+1)}^{\frac{2}{3}}?$$

Commented by MJS_new last updated on 05/Nov/20

$$\mathrm{because}\mathrm{key}[+]\mathrm{very}\mathrm{close}\mathrm{to}\mathrm{key}[\left(\right]\mathrm{on}$$$$\mathrm{display}\mathrm{and}\mathrm{typing}\mathrm{in}\mathrm{jolting}\mathrm{bus}$$

Commented by bramlexs22 last updated on 05/Nov/20

����������

Answered by bobhans last updated on 05/Nov/20

$$\eta =\int \frac{dx}{x^3{\left(x^6(1+x^{-6})\right)}^{\frac{2}{3}}}$$$$\eta =\int \frac{dx}{x^7{(1+x^{-6})}^{\frac{2}{3}}}$$$$\eta =\int \frac{x^{-7}dx}{{(1+x^{-6})}^{\frac{2}{3}}};[t=1+x^{-6}]$$$$\eta =-\frac{1}{6}\int \frac{dt}{t^{2/3}}=-\frac{1}{6}\int t^{-2/3}dt$$$$\eta =-\frac{1}{2}{t}^{1/3}+c=-\frac{1}{2}\sqrt[3]{1+x^{-6}}+c$$

Commented by MJS_new last updated on 05/Nov/20

$$\mathrm{also}\mathrm{very}\mathrm{nice}!$$

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