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Question Number 168291 by MikeH last updated on 07/Apr/22
$$\int{t}^{\mathrm{7}} \mathrm{sin}\left({t}^{\mathrm{7}} \right){dt} \\ $$
Answered by Engr_Jidda last updated on 07/Apr/22
$${let}\:{t}^{\mathrm{7}} ={x}\:{then}\:{dt}=\mathrm{7}{t}^{\mathrm{6}} {dx} \\ $$$$\therefore\:\int{t}^{\mathrm{7}} {sin}\left({t}^{\mathrm{7}} \right){dt}=\int\mathrm{7}{xsinx}\left({x}^{−\mathrm{1}} \right){dx} \\ $$$$=\mathrm{7}\int{sinxdx}=−\mathrm{7}{cosx}\:{OR}\:−\mathrm{7}{cos}\left({t}^{\mathrm{7}} \right) \\ $$
Answered by Florian last updated on 07/Apr/22
$${It}'{s}\:\:{integral}\:{has}\:{no}\:{elementary}\:{primitive}! \\ $$
Commented by MikeH last updated on 08/Apr/22
$$\mathrm{wow}\:\mathrm{really}? \\ $$
Commented by Florian last updated on 08/Apr/22
$${Yes}! \\ $$