Question Number 88097 by sahnaz last updated on 08/Apr/20
$$\int\frac{\mathrm{dx}}{\left(\mathrm{2x}−\mathrm{3}\right)^{\frac{\mathrm{2}}{\mathrm{3}}} } \\ $$
Answered by john santu last updated on 08/Apr/20
![∫ t^(−2/3) ×(1/2)dt [ t = 2x−3 ] = (1/2)×3 × (t)^(1/(3 )) + c = (3/2)((2x−3))^(1/(3 )) + c](https://www.tinkutara.com/question/Q88106.png)
$$\int\:{t}^{−\mathrm{2}/\mathrm{3}} ×\frac{\mathrm{1}}{\mathrm{2}}{dt}\:\:\:\left[\:{t}\:=\:\mathrm{2}{x}−\mathrm{3}\:\right] \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{2}}×\mathrm{3}\:×\:\sqrt[{\mathrm{3}\:\:}]{{t}}\:+\:{c}\: \\ $$$$=\:\frac{\mathrm{3}}{\mathrm{2}}\sqrt[{\mathrm{3}\:\:\:}]{\mathrm{2}{x}−\mathrm{3}}\:+\:{c}\: \\ $$