I don't know how to find this general antiderivative. I have tried everything I could think of.

Question

Find the general antiderivative. Use C for the constant of integration.

g(θ) = sec(5θ)tan(5θ)

In my notes I have that secxtanx has the antiderivative of secx so I thought the theory applies no matter what x is which is why I put sec(5θ)+C, but that was wrong. I thought I should use the rule because another example in my notes did so then I put sec(5θ)*5+C but that was wrong as well so I am a little stuck.

 

Answer 1

You know that       d/dx[sec(x)] = sec(x)tan(x)

 

∫sec(5θ)tan(5θ)dθ = (1/5)sec(5θ) + C

 

 

You take the derivative of the result, you will get back the integrand.

 

With integration problems like these, it is best to perform a guess and check.  This takes realization and knowledge of your general derivatives.