Tìm ∫xex2+1dx

Question

Tìm \(\int x{\rm e}^{x^{2} +1} {\rm d}x .\)

 A. \({\rm e}^{x^{2} +1} +C. \)

B. \(\frac{1}{2} {\rm e}^{x^{2} } +C. \)

C. \(\frac{1}{2} {\rm e}^{x^{2} +1} +C.  \)

D. \(\frac{1}{2} {\rm e}^{x^{2} -1} +C.\)

Answer 1

Chọn C

 Ta có:\( \int x{\rm e}^{x^{2+1} } {\rm d}x =\frac{1}{2} \int {\rm e}^{x^{2} +1} {\rm d(}x^{2} +1{\rm )} =\frac{1}{2} {\rm e}^{x^{2} +1} +C\)