Intergarting: e^(sin(x))*(cos(x)x+1)

[GeorgeJBrooks]

How do I integrate: e^(sin(x))*(cos(x)x+1) to get x*e^sin(x)

I tried using integration by parts a few times and ended up with: e^sin(x)(xsin(x)+cos(x))+xcos(x)+sin(x)+x+c (I may have made errors in here) but the answer i'm looking for is x*e^sin(x) which i'm not getting anywhere near.

 

[Ishuda]

How do I integrate: e^(sin(x))*(cos(x)x+1) to get x*e^sin(x)

I tried using integration by parts a few times and ended up with: e^sin(x)(xsin(x)+cos(x))+xcos(x)+sin(x)+x+c (I may have made errors in here) but the answer i'm looking for is x*e^sin(x) which i'm not getting anywhere near.

\(\displaystyle \int \, e^{sin(x)} \,\left( cos(x) x\, +\, 1\right)\, dx\, =\, \int\, x \left[cos(x) e^{sin(x)}\right]\, dx \,+\, \int \,e^{sin(x)}\, dx\)

\(\displaystyle \int\, x \left[cos(x)\, e^{sin(x)}\right]\, dx\, = \,\int \,u [v]\, dx \)