Integration Questions

Question Number 5422 by love math last updated on 14/May/16

$$\int_{\mathrm{0}} ^{\frac{\mathrm{7}}{\mathrm{2}}} \left({x}+\mathrm{1}\right)\left(\mathrm{2}{x}+\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} {dx} \\$$

Answered by nchejane last updated on 14/May/16

$$=\left[\frac{\mathrm{3}}{\mathrm{8}}\left({x}+\mathrm{1}\right)\left(\mathrm{2}{x}+\mathrm{1}\right)^{\frac{\mathrm{4}}{\mathrm{3}}} \right]_{\mathrm{0}} ^{\frac{\mathrm{7}}{\mathrm{2}}} −\frac{\mathrm{3}}{\mathrm{8}}\int_{\mathrm{0}} ^{\frac{\mathrm{7}}{\mathrm{2}}} \left(\mathrm{2}{x}+\mathrm{1}\right)^{\frac{\mathrm{4}}{\mathrm{3}}} {dx} \\$$$$=\left[\frac{\mathrm{3}}{\mathrm{8}}\left({x}+\mathrm{1}\right)\left(\mathrm{2}{x}+\mathrm{2}\right)^{\frac{\mathrm{4}}{\mathrm{3}}} \right]_{\mathrm{0}} ^{\frac{\mathrm{7}}{\mathrm{2}}} −\left[\frac{\mathrm{9}}{\mathrm{28}}\left(\mathrm{2}{x}+\mathrm{1}\right)^{\frac{\mathrm{7}}{\mathrm{3}}} \right]_{\mathrm{0}} ^{\frac{\mathrm{7}}{\mathrm{2}}} \\$$$$=.... \\$$