Question

$\int x^2 e^{x^3}\, dx$ equals
(A)$\frac 13 e^{x^3}+C$
(B)$\frac 13 e^{x^2}+C$
(C)$\frac 12 e^{x^3}+C$
(D)$\frac 12 e^{x^2}+C$

Answer 1

check the attachment

Answer 2

Answer:

None of the option is correct

Step-by-step explanation:

To integrate

$\int x^2 e^{x^3}\, dx$

one can analyse that we can integrate it by substitution Method.

$put \: {x}^{3} = z \\ \\ 3 {x}^{2} dx = dz \\ \\ {x}^{2} dx = \frac{dz}{3}$

Substitute these values into integration

$\int\frac{1}{3} {e}^{z} dz \\ \\ \frac{1}{3} \int {e}^{z} dz \\ \\ \because \: \int {e}^{x} dx \: = {e}^{x} + c \\ \\ so \\ \\ = \frac{ {e}^{z} }{3} + c \\ \\ undo \: substitution \\ \\ \int x^2 e^{x^3}\, dx= \frac{ {e}^{ {x}^{3} } }{3} + c$