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Find the integral $\int\frac{x}{e^{\frac{x}{2}}}dx$

Step-by-step Solution

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sin
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asin
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sinh
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asinh
acosh
atanh
acoth
asech
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Final Answer

$-2e^{\frac{-x}{2}}x-4e^{\frac{-x}{2}}+C_0$
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Step-by-step Solution

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1

Rewrite the exponent using the power rule $\frac{a^m}{a^n}=a^{m-n}$, where in this case $m=0$

$\int xe^{-\frac{x}{2}}dx$

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

$\int xe^{-\frac{x}{2}}dx$

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Learn how to solve integrals of exponential functions problems step by step online. Find the integral int(x/(e^(x/2)))dx. Rewrite the exponent using the power rule \frac{a^m}{a^n}=a^{m-n}, where in this case m=0. Multiplying the fraction by -1. We can solve the integral \int xe^{\frac{-x}{2}}dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify u and calculate du.

Final Answer

$-2e^{\frac{-x}{2}}x-4e^{\frac{-x}{2}}+C_0$

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Function Plot

Plotting: $-2e^{\frac{-x}{2}}x-4e^{\frac{-x}{2}}+C_0$

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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
|◻|
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:

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

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