ðŸ‘‰ Try now NerdPal! Our new math app on iOS and Android

# Find the integral $\int y^{-1}e^ydy$

Go!
Symbolic mode
Text mode
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
|◻|
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

##  Final answer to the problem

$Ei\left(y\right)+C_0$
Got another answer? Verify it here!

##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• 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
Can't find a method? Tell us so we can add it.
1

Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number

$\int\frac{1}{y}e^ydy$

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

$\int\frac{1}{y}e^ydy$

Learn how to solve integrals of exponential functions problems step by step online. Find the integral int(y^(-1)e^y)dy. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. Multiplying the fraction by e^y. The integral \int\frac{e^y}{y}dy is called 'exponential integral' and is non-elementary. The formula for the exponential integral is: \int\frac{e^x}{x}=Ei(x), where Ei is a special function on the complex plane. As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration C.

##  Final answer to the problem

$Ei\left(y\right)+C_0$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SnapXam A2

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
|◻|
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

###  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.