# Step-by-step Solution

Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

## Step-by-step explanation

Problem to solve:

$\int\:x^2\:e^{-3x}dx$

Learn how to solve limits by direct substitution problems step by step online.

$\begin{matrix}u=e^{-3x} \\ du=-3e^{-3x}dx\end{matrix}$

Learn how to solve limits by direct substitution problems step by step online. Compute the integral int(x^2*2.718281828459045^(-3*x))dx. Solve the integral \int x^2e^{-3x}dx applying u-substitution. Let u and du be. Isolate dx in the previous equation. Rewriting x in terms of u. Substituting u, dx and x in the integral and simplify.

$-\frac{1}{27}\left(e^{-3x}\left(-3x\right)^2-2\left(-3e^{-3x}x-e^{-3x}\right)\right)+C_0$

### Problem Analysis

$\int\:x^2\:e^{-3x}dx$

### Main topic:

Limits by direct substitution

~ 3.37 seconds