∫1+xexsin2xexdx=
-cotex+C
tanxex+C
tanex+C
cotxex+C
-cotxex+C
Explanation for Correct answer:
Finding the value of the given integral:
The given equation is ∫1+xexsin2xexdx
Solving this by using the substitution method
t=xexdt=xex+1.exdx∵ddxuv=u.dv+v.du
∫1+xexsin2xexdx=∫dtsin2t=∫cosec2tdt=-cott+C=-cotxex+C
Hence, option (E) is the correct answer.