How do you integrate $e^7x^3 x^2 dx$ ?

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Answer 1 · 2016-08-15T17:54:20

$=(e^7)/6 (x^6) +C$

$int e^7x^3x^2 \dx$

I can see two approaches 1) combining the $x$ terms or 2) doing u substitution. first lets express this differently by moving out the constant

$e^7int x^3x^2 \dx$
1)

$e^7int x^5\dx$
$(e^7)/6 (x^6)+C$

2)
now i will use u substitution and let $u=x^3$ then
$(du)/(dx) =3x^2$
$1/3du=x^2 dx$

now substituting this back in
$e^7int u1/3 \du$
$(e^7)/3int u \du$

$=(e^7)/3 (u^2)/2 +C$
now we place replace u
$=(e^7)/6 (x^3)^2 +C$
$=(e^7)/6 (x^6) +C$

How do you integrate e^7x^3 x^2 dxe^7x^3 x^2 dx?