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

Step-by-step Solution

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e
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ln
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sin
cos
tan
cot
sec
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asin
acos
atan
acot
asec
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sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Final answer to the problem

$\frac{e^yx}{y}+C_0$
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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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1

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

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

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

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Learn how to solve integrals of exponential functions problems step by step online. Find the integral int(y^(-1)e^y)dx. 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 of a constant is equal to the constant times the integral's variable. Multiplying the fraction by x.

Final answer to the problem

$\frac{e^yx}{y}+C_0$

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Function Plot

Plotting: $\frac{e^yx}{y}+C_0$

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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

See formulas (1)

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