Question Number 192858 by josemate19 last updated on 29/May/23
$$\int_{\mathrm{4}{x}} ^{\:{x}^{\mathrm{3}} } \sqrt{\sqrt{{t}}+{t}^{\mathrm{1}/\mathrm{3}} }{dt} \\ $$
Answered by Frix last updated on 29/May/23
$$\int\sqrt{\sqrt{{t}}+\sqrt[{\mathrm{3}}]{{t}}}{dt}= \\ $$$$=\frac{\mathrm{4}\sqrt{\mathrm{1}+\sqrt[{\mathrm{6}}]{{t}}}}{\mathrm{15015}}\left(\mathrm{3003}{t}^{\frac{\mathrm{7}}{\mathrm{6}}} +\mathrm{231}{t}−\mathrm{252}{t}^{\frac{\mathrm{5}}{\mathrm{6}}} +\mathrm{280}{t}^{\frac{\mathrm{2}}{\mathrm{3}}} −\mathrm{320}{t}^{\frac{\mathrm{1}}{\mathrm{2}}} +\mathrm{384}{t}^{\frac{\mathrm{1}}{\mathrm{3}}} −\mathrm{512}{t}^{\frac{\mathrm{1}}{\mathrm{6}}} +\mathrm{1024}\right)\:+{C} \\ $$$$\mathrm{Now}\:\mathrm{do}\:\mathrm{me}\:\mathrm{a}\:\mathrm{favour}\:\mathrm{and}\:\mathrm{insert}\:\mathrm{the}\:\mathrm{borders} \\ $$$$\mathrm{for}\:\mathrm{yourself}! \\ $$