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Find the integral $\int xe^{-x}dx$

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Solution

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Final answer to the problem

$-e^{-x}x-e^{-x}+C_0$
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Step-by-step Solution

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  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Integrate using trigonometric identities
  • Integrate using basic integrals
  • Product of Binomials with Common Term
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We can solve the integral $\int xe^{-x}dx$ by applying integration by parts method to calculate the integral of the product of two functions, using the following formula

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

Learn how to solve integrals of exponential functions problems step by step online.

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

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Unlock the first 3 steps of this solution

Learn how to solve integrals of exponential functions problems step by step online. Find the integral int(xe^(-x))dx. We can solve the integral \int xe^{-x}dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify or choose u and calculate it's derivative, du. Now, identify dv and calculate v. Solve the integral to find v.

Final answer to the problem

$-e^{-x}x-e^{-x}+C_0$

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Function Plot

Plotting: $-e^{-x}x-e^{-x}+C_0$

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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
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Similar Problems Solved

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$\int\frac{1}{e^{2x}-3e^x}dx$

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$\int\frac{1}{1+e^{-2x}}dx$

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$\int x^2e^xdx$

Find the integral

$\int16xe^{4x}dx$

Find the integral

$\int xe^{3x}dx$

Find the integral

$\int xe^{2x}dx$

Main Topic: Integrals of Exponential Functions

Those are integrals that involve exponential functions. Recall that an exponential function is a function of the form f(x)=a^x.

Used Formulas

See formulas (4)

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