Question Number 83115 by 09658867628 last updated on 28/Feb/20
$$\int\mathrm{cos}\:{xe}^{\mathrm{sin}\:{x}} {dx} \\ $$
Commented by niroj last updated on 28/Feb/20
$$ \\ $$$$\:\int\boldsymbol{\mathrm{cos}}\:\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{sin}}\:\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{dx}} \\ $$$$\:\:\int\:\mathrm{e}^{\mathrm{sin}\:\mathrm{x}} \:\mathrm{cos}\:\mathrm{x}\:\mathrm{dx} \\ $$$$\:\:\mathrm{Put}\:\mathrm{sin}\:\mathrm{x}=\:\mathrm{t} \\ $$$$\:\:\:\:\:\:\:\mathrm{cos}\:\mathrm{xdx}=\mathrm{dt} \\ $$$$\:\:\:\int\:\mathrm{e}^{\mathrm{t}} .\:\mathrm{dt}=\:\mathrm{e}^{\mathrm{t}} \:+\mathrm{C} \\ $$$$\:\:\:\mathrm{e}^{\mathrm{sin}\:\mathrm{x}} +\mathrm{C}\:// \\ $$
Answered by som(math1967) last updated on 28/Feb/20
$$\int{e}^{{sinx}} {d}\left({sinx}\right)={e}^{{sinx}} +{C} \\ $$