Integral of tan^n (x) dx

[mario99]

[math]\int tan^n x \ dx[/math]


Any help would be appreciated.

 

[topsquark]

[math]\int tan^n x \ dx[/math]


Any help would be appreciated.

Hint: Start with
[imath]\displaystyle \int tan^n(x) \, dx = \int tan^{n - 2}(x) \, tan^2(x) \, dx = \int tan^{n - 2}(x) \, ( sec^2(x) - 1 ) \, dx[/imath]

Give it a try and post your results.

-Dan

 

[mario99]

Hint: Start with
[imath]\displaystyle \int tan^n(x) \, dx = \int tan^{n - 2}(x) \, tan^2(x) \, dx = \int tan^{n - 2}(x) \, ( sec^2(x) - 1 ) \, dx[/imath]

Give it a try and post your results.

-Dan

Thank you topsquark for helping me.

How did you figure out this idea? How to choose [imath]\theta[/imath] and [imath]\phi[/imath] in this case?

 

[khansaheb]

How did you figure out this idea? How to choose θ\thetaθ and ϕ\phiϕ in this case?

Where/How are Θ and Φ are coming inhere? In OP you have 'x' as the independent variable. No substitutions were made - yet.

 

[khansaheb]

How did you figure out this idea?

\(\displaystyle \frac{d}{dx} tan(x) = sec^2(x)\) ...............and

\(\displaystyle tan^2(x) = sec^2(x) - 1 \)

 

[topsquark]

Thank you topsquark for helping me.

How did you figure out this idea? How to choose [imath]\theta[/imath] and [imath]\phi[/imath] in this case?

I learned it from a book. Give it a try.

-Dan

 

[khansaheb]

I learned it from a book. Give it a try.

-Dan

I learnt in class-room and wrote it down as class-notes.

 

[Steven G]

I saw it in class and then went home and derived it on my own a few times. It really wasn't that bad!