Antiderivatives.What is the antiderivative of sin3x?

Expert Answers
justaguide eNotes educator| Certified Educator

We have to find the anti derivative of sin 3x

Int [ sin 3x dx]

Let 3x = y => dx = dy / 3

=> Int [ (1/3)*sin y dy]

=> (1/3)*(-cos y)

=> (-1/3)* cos 3x + C

The anti derivative is (-1/3)* cos 3x + C

giorgiana1976 | Student

To find the antiderivative of sin 3x, we'll have to determine the indefinite integral of sin 3x.

Int sin 3x dx

We'll substitute 3x by t.

3x = t

We'll differentiate both sides:

3dx = dt

We'll divide by 3:

dx = dt/3

We'll re-write the integral of the function , changing the variable x to t:

Int sin t*(dt/3) = (1/3)*Int sin t dt

(1/3)*Int sin t dt = - cos t/3 +C

We'll substitute t by 3x:

Int sin 3x dx =  - (cos 3x)/3 +C

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