Integrate sin(3x)

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

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Answer

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

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

Add the constant of integration

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

Answer

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

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Problem Analysis

Main topic:

Integration by substitution

Time to solve it:

0.22 seconds

Views:

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