- Thread starter
- #1

- Thread starter shamieh
- Start date

- Thread starter
- #1

Your formula is incorrect.

[tex]\int\tan^n\!x\,dx \;=\;\frac{\tan^{n-1}\!x}{n - 1} - \int\tan^{n-2}\!x\,dx[/tex]

Example: .[tex]\int\tan^4\!x\,dx[/tex]

Substitute [tex]n=4[/tex] into the formula:

[tex]\int\tan^4\!x\,dx \;=\;\tfrac{1}{3}\tan^3\!x - \int \tan^2\!x\,dx[/tex]

. . . . . . . . . [tex]=\;\tfrac{1}{3}\tan^3\!x - \int(\sec^2\!x -1)\,dx [/tex]

. . . . . . . . . [tex]=\;\tfrac{1}{3}\tan^3\!x - \int\sec^2\!x\,dx + \int dx[/tex]

. . . . . . . . . [tex]=\;\tfrac{1}{3}\tan^3\!x - \tan x + x + C[/tex]

- Thread starter
- #3