The given integration is,
∫ x 2 e x 3 dx
Assume, x 3 =t
Differentiate with respect to x.
3 x 2 = dt dx dx= dt 3 x 2
Substitute the values in integration, we get,
∫ x 2 e x 3 dx = ∫ x 2 e t dt 3 x 2 = ∫ e t 3 dt = e t 3 +C
Now, substitute the value of t in the above equation, we get,
∫ x 2 e x 3 dx = e x 3 3 +C
Therefore, Option (A) is correct.
equals
A. − cot (exx) + C
B. tan (xex) + C
C. tan (ex) + C
D. cot (ex) + C