Question

integration of e^sinx×cosx

Answer 1

if we differentiate
${e}^{ \sin(x)}$
with respect to x, we get
${e}^{sinx} cosx$
hence on integrating
${e}^{sinx} cosx$

we get
${e}^{sinx }$

Answer 2

if we differentiate 
{e}^{\sin(x)}esin(x) 
with respect to x, we get 
{e}^{sinx} cosxesinxcosx 
hence on integrating 
{e}^{sinx} cosxesinxcosx 

we get 
{e}^{sinx }esinx 

Thus, it is derived