- #1
tandoorichicken
- 245
- 0
How do you integrate tan(3x)?
As in
[tex] \int \tan{3x} \,dx [/tex]
As in
[tex] \int \tan{3x} \,dx [/tex]
The integration of tan(3x) involves using the substitution method. We substitute u = 3x and du = 3dx, then rewrite the integral in terms of u.
The general formula for integrating tan(3x) is ∫ tan(ax) dx = ln|sec(ax)|/a + C, where a is the coefficient of x.
Yes, you can use trigonometric identities such as tan(x) = sin(x)/cos(x) and sec(x) = 1/cos(x) to rewrite tan(3x) in a form that is easier to integrate.
One specific rule for integrating tan(3x) is that you must separate the integral into two parts, one containing only sin(3x) and the other containing only cos(3x). This will make the integration process easier.
The limits of integration for tan(3x) depend on the specific problem or context. You can determine the limits by looking at the given interval or by using the substitution method to solve the integral.