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Question Number 72112 by A8;15: last updated on 24/Oct/19

Answered by mind is power last updated on 24/Oct/19

$$\mathrm{x}=\frac{1}{\mathrm{t}}\Rightarrow \mathrm{dx}=\frac{-\mathrm{dt}}{{\mathrm{t}}^2}$$$$\frac{\frac{1}{{\mathrm{t}}^{899999999}}}{\frac{{(1+{\mathrm{t}}^9)}^{1000000001}}{{\mathrm{t}}^{900000009}}}.\frac{-\mathrm{dt}}{{\mathrm{t}}^2}=\frac{-{\mathrm{t}}^8\mathrm{dt}}{{(1+{\mathrm{t}}^9)}^{1000000001}}=\frac{1}{9000000000}\frac{1}{{(1+{\mathrm{t}}^9)}^{1000000000}}+\mathrm{c}$$$$\mathrm{t}=\frac{1}{\mathrm{x}\Rightarrow }$$$$\int \frac{{\mathrm{x}}^{899999999}}{{(1+{\mathrm{x}}^9)}^{1000000001}}\mathrm{dx}=\frac{1}{9000000000}\frac{{\mathrm{x}}^{900000000}}{{({\mathrm{x}}^9+1)}^{1000000000}}+\mathrm{c}$$

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