# Step-by-step Solution

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
|◻|
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

## Step-by-step explanation

Problem to solve:

$\int\cos\left(4x\right)e^{3x}dx$

Learn how to solve equations problems step by step online.

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

Learn how to solve equations problems step by step online. Solve the trigonometric integral int(cos(4*x)*2.718281828459045^(3*x))dx. Use the integration by parts theorem to calculate the integral \int e^{3x}\cos\left(4x\right)dx, using the following formula. First, identify u and calculate du. Now, identify dv and calculate v. Solve the integral.

$-\frac{81}{175}\left(\frac{1}{3}e^{3x}\cos\left(4x\right)+\frac{4}{9}e^{3x}\sin\left(4x\right)-\frac{16}{27}e^{3x}\cos\left(4x\right)-\frac{64}{81}e^{3x}\sin\left(4x\right)\right)+C_0$

### Problem Analysis

$\int\cos\left(4x\right)e^{3x}dx$

Equations

~ 0.57 seconds