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# Find the integral $\int e^x\cos\left(x\right)dx$

## Step-by-step Solution

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e
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ln
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sin
cos
tan
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asin
acos
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sinh
cosh
tanh
coth
sech
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asinh
acosh
atanh
acoth
asech
acsch

###  Videos

$\frac{1}{2}e^x\cos\left(x\right)+\frac{1}{2}e^x\sin\left(x\right)+C_0$
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## Step-by-step Solution

Problem to solve:

$\int\left(e^x\:\cos\left(x\right)\right)dx$

Specify the solving method

1

We can solve the integral $\int e^x\cos\left(x\right)dx$ by applying integration by parts method to calculate the integral of the product of two functions, using the following formula

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$
2

First, identify $u$ and calculate $du$

$\begin{matrix}\displaystyle{u=\cos\left(x\right)}\\ \displaystyle{du=-\sin\left(x\right)dx}\end{matrix}$

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

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

Learn how to solve integrals of exponential functions problems step by step online. Find the integral int(e^xcos(x))dx. We can solve the integral \int e^x\cos\left(x\right)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. Now, identify dv and calculate v. Solve the integral.

$\frac{1}{2}e^x\cos\left(x\right)+\frac{1}{2}e^x\sin\left(x\right)+C_0$

##  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 int(e^xcos(x))dx using basic integralsSolve int(e^xcos(x))dx using u-substitutionSolve int(e^xcos(x))dx using integration by parts
SnapXam A2

### beta Got a different answer? Verify it!

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

$\int\left(e^x\:\cos\left(x\right)\right)dx$