# Integrate sin(3x)

## \int\sin\left(3x\right)dx

Go!
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
2

e
π
ln
log
lim
d/dx
d/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

$-\frac{1}{3}\cos\left(3x\right)+C_0$

## Step by step solution

Problem

$\int\sin\left(3x\right)dx$
1

Solve the integral $\int\sin\left(3x\right)dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=3x \\ du=3dx\end{matrix}$
2

Isolate $dx$ in the previous equation

$\frac{du}{3}=dx$
3

Substituting $u$ and $dx$ in the integral

$\int\frac{\sin\left(u\right)}{3}du$
4

Taking the constant out of the integral

$\frac{1}{3}\int\sin\left(u\right)du$
5

Apply the integral of the sine function

$\frac{1}{3}\left(-1\right)\cos\left(u\right)$
6

Substitute $u$ back for it's value, $3x$

$-\frac{1}{3}\cos\left(3x\right)$
7

$-\frac{1}{3}\cos\left(3x\right)+C_0$

$-\frac{1}{3}\cos\left(3x\right)+C_0$

### Struggling with math?

Access detailed step by step solutions to millions of problems, growing every day!

### Main topic:

Integration by substitution

0.22 seconds

79