# How do you integrate int sin2x dx?

Then teach the underlying concepts
Don't copy without citing sources
preview
?

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

71
sente Share
Dec 17, 2016

$\int \sin \left(2 x\right) \mathrm{dx} = - \frac{1}{2} \cos \left(2 x\right) + C$

#### Explanation:

Using integration by substitution together with the known integral $\int \sin \left(x\right) \mathrm{dx} = - \cos \left(x\right) + C$, we first let $u = 2 x \implies \mathrm{du} = 2 \mathrm{dx}$. Then

$\int \sin \left(2 x\right) \mathrm{dx} = \frac{1}{2} \int \sin \left(2 x\right) 2 \mathrm{dx}$

$= \frac{1}{2} \int \sin \left(u\right) \mathrm{du}$

$= \frac{1}{2} \left(- \cos \left(u\right)\right) + C$

$= - \frac{1}{2} \cos \left(2 x\right) + C$

• 11 minutes ago
• 11 minutes ago
• 11 minutes ago
• 17 minutes ago
• A minute ago
• 4 minutes ago
• 4 minutes ago
• 4 minutes ago
• 5 minutes ago
• 8 minutes ago
• 11 minutes ago
• 11 minutes ago
• 11 minutes ago
• 17 minutes ago