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# Find the integral $\int3e^y\cos\left(e^y\right)dy$

## Step-by-step Solution

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###  Videos

$3\sin\left(e^y\right)+C_0$
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##  Step-by-step Solution 

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The integral of a function times a constant ($3$) is equal to the constant times the integral of the function

$3\int e^y\cos\left(e^y\right)dy$

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

$3\int e^y\cos\left(e^y\right)dy$

Learn how to solve integrals of exponential functions problems step by step online. Find the integral int(3e^ycos(e^y))dy. The integral of a function times a constant (3) is equal to the constant times the integral of the function. We can solve the integral \int e^y\cos\left(e^y\right)dy by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that e^y it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dy in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above. Isolate dy in the previous equation.

$3\sin\left(e^y\right)+C_0$

##  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

Solve integral of 3e^ydy using basic integralsSolve integral of 3e^ydy using u-substitutionSolve integral of 3e^ydy using integration by parts

SnapXam A2

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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

### 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.