Question Number 64270 by aliesam last updated on 16/Jul/19
$$\int\frac{\mathrm{5}{sin}\left({x}\right)\:{cos}\left({x}\right)}{\:\sqrt[{\mathrm{3}}]{{cos}\left({x}\right)+\mathrm{1}}}\:{dx} \\ $$
Answered by Tanmay chaudhury last updated on 16/Jul/19
$${t}^{\mathrm{3}} =\mathrm{1}+{cosx}\:\:\mathrm{3}{t}^{\mathrm{2}} {dt}=−{sinxdx} \\ $$$$\int\frac{\mathrm{5}×\left({t}^{\mathrm{3}} −\mathrm{1}\right)×−\mathrm{3}{t}^{\mathrm{2}} {dt}}{{t}} \\ $$$$−\mathrm{15}\int\left({t}^{\mathrm{4}} −{t}\right){dt} \\ $$$$=\left(−\mathrm{15}\right)×\left\{\frac{{t}^{\mathrm{5}} }{\mathrm{5}}−\frac{{t}^{\mathrm{2}} }{\mathrm{2}}\right\}+{c} \\ $$$$=−\mathrm{3}{t}^{\mathrm{5}} +\frac{\mathrm{15}}{\mathrm{2}}{t}^{\mathrm{2}} +{c} \\ $$$$=−\mathrm{3}\left(\mathrm{1}+{cosx}\right)^{\frac{\mathrm{5}}{\mathrm{3}}} +\frac{\mathrm{15}}{\mathrm{2}}\left(\mathrm{1}+{cosx}\right)^{\frac{\mathrm{2}}{\mathrm{3}}} +{c} \\ $$
Commented by Prithwish sen last updated on 16/Jul/19
$$\mathrm{Tanmay}\:\mathrm{sir}.\:\mathrm{Is}\:\mathrm{it}\:\mathrm{you}\:?\:\mathrm{Happy}\:\mathrm{to}\:\mathrm{see}\:\mathrm{you}\:\mathrm{sir}. \\ $$$$\mathrm{please}\:\mathrm{don}'\mathrm{t}\:\mathrm{leave}. \\ $$
Commented by Tawa1 last updated on 16/Jul/19
$$\mathrm{Sir}\:\mathrm{tanmay},\:\mathrm{were}\:\mathrm{have}\:\mathrm{you}\:\mathrm{been}.\:\mathrm{Hope}\:\mathrm{you}\:\mathrm{are}\:\mathrm{good} \\ $$
Commented by aliesam last updated on 16/Jul/19
$${i}\:{am}\:{so}\:{happy}\:{to}\:{see}\:{you}\:{again}\:{sir}\:{and}\:{thank}\:{you}\:{for}\:{the}\:{sol} \\ $$
Commented by Tanmay chaudhury last updated on 16/Jul/19
$${this}\:{platform}\:{provide}\:{food}\:{of}\:{brain}\:{so}\:{i}\:{can}\:{not} \\ $$$${stay}\:{starved} \\ $$
Commented by Tawa1 last updated on 16/Jul/19
$$\mathrm{Hahahaha}.\:\mathrm{welcome}\:\mathrm{sir} \\ $$
Commented by Prithwish sen last updated on 16/Jul/19
$$\mathrm{Sir}\:\mathrm{are}\:\mathrm{you}\:\mathrm{from}\:\mathrm{kolkata}\:? \\ $$
Commented by Tanmay chaudhury last updated on 16/Jul/19
$${ha}\:{ami}\:{barrakcpore}\:{a}\:{thaki} \\ $$
Commented by Prithwish sen last updated on 16/Jul/19
$$\mathrm{ami}\:\mathrm{tribeni}.\mathrm{kono}\:\mathrm{din}\:\mathrm{dekha}\:\mathrm{hobe}.\:\mathrm{barrackpure}\: \\ $$$$\mathrm{amar}\:\mathrm{mamar}\:\mathrm{bari} \\ $$
Commented by Tanmay chaudhury last updated on 16/Jul/19
$${achha}\:{thik}\:{ache}..{bhalo}\:{thakun}.. \\ $$
Commented by Prithwish sen last updated on 16/Jul/19
$$\mathrm{apnio}. \\ $$