Question

please solve this question ..
step by step please​

Answer 1

I hope this answer helps you

Answer 2

Answer:

$\huge\pink{\boxed{\blue{\boxed{ \purple{ \boxed{{\pink{Answer}}}}}}}} \\ \large\pink{\boxed{\blue{\boxed{ \purple{ \boxed{{\pink{Your~answer↓}}}}}}}} \\ \\ evaluate ∫  {2x}^{3} { {e}^{x} }^{2} dx \\ =  ∫( x \times {2x}^{2} { {e}^{x} }^{2}) dx \\ =  ∫  {e}^{ {x}^{2}} {(x)}^{2} \times 2xdx\\ \small\bold\red{(put \: {x}^{2} = t \: = > \: 2xdx = dt) }\\ =  ∫  {e}^{t} tdt \\\small\bold\red{using \: integration \: by \: parts} \\ = t ∫{e}^{t} dt - ∫ (\frac{d}{dt} t  (∫  {e}^{t} dt))dt \\ = t {e}^{t} -  ∫  {e}^{t} dt \\ = t {e}^{t} - {e}^{t} + c \\ = {e}^{t} (t - 1) + c \\ = {e}^{ {x}^{2} } ( {x}^{2} - 1) + c$

$\huge \fcolorbox{black}{cyan}{♛hope \: it \: helps \: you♛}$