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Question Number 167006 by cortano1 last updated on 04/Mar/22

$$\int \frac{{3\mathrm{x}}^3}{{(\mathrm{x}-1)}^3}\mathrm{dx}=?$$

Answered by MJS_new last updated on 04/Mar/22

$$\int \frac{3x^3}{{(x-1)}^3}dx=\int \frac{3{(t+1)}^3}{t^3}dt=$$$$=\int (3+\frac{9}{t}+\frac{9}{t^2}+\frac{3}{t^3})dt=$$$$=3t+9\ln t-\frac{9}{t}-\frac{3}{2t^2}=$$$$=\frac{2(2t^3-6t-1)}{2t^2}+9\ln t=$$$$=\frac{3(2x^3-6x^2+3)}{2{(x-1)}^2}+9\ln \mid x-1\mid +C$$

Commented by peter frank last updated on 04/Mar/22

$$\mathrm{thank}\mathrm{you}$$

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