## anonymous 4 years ago the integral of tan(3x) dx with upper limit pie/3 and lower limit pie/4

1. anonymous

Put, u = 3x and du = 3dx .The integrand simplifies to $1/3\int\limits \tan(u) du$ = -1/3 log(cos(u))+constant = -1/3 log(cos(3 x))+constant(Substituting back)

2. anonymous

Now you can just plug in the limits.

3. anonymous

With limits it will become $-\ln (2)/6 ~~0.115525$

4. mathmate

−ln(2)/6= -0.115525