- #1
SpicyPepper
- 20
- 0
I'm not sure if my answer is just wrong or basically the same as the one in the back of my book.
[tex]\int tan^5(x)dx[/tex]
My answer:
[tex]\int tan^5(x)dx = \frac{tan^4(x)}{4} - \int(sec^2(x)tan(x) - tan(x)) dx[/tex]
[tex]\int tan^5(x)dx = \frac{tan^4(x)}{4} - \frac{tan^2(x)}{2} + ln|sec(x)| + C[/tex]
Book answer:
[tex]\int tan^5(x)dx = \frac{sec^4(x)}{4} - tan^2(x) + ln|sec(x)| + C[/tex]
If I understand correctly,
[tex]\frac{tan^4(x)}{4} + C = \frac{sec^4(x) - 1}{4} + C = \frac{sec^4(x)}{4} + C[/tex]
If that's wrong let me know please.
However, I don't get why I keep getting
[tex]\frac{tan^2(x)}{2}[/tex]
instead of
[tex]tan^2(x)[/tex]
Homework Statement
[tex]\int tan^5(x)dx[/tex]
The Attempt at a Solution
My answer:
[tex]\int tan^5(x)dx = \frac{tan^4(x)}{4} - \int(sec^2(x)tan(x) - tan(x)) dx[/tex]
[tex]\int tan^5(x)dx = \frac{tan^4(x)}{4} - \frac{tan^2(x)}{2} + ln|sec(x)| + C[/tex]
Book answer:
[tex]\int tan^5(x)dx = \frac{sec^4(x)}{4} - tan^2(x) + ln|sec(x)| + C[/tex]
If I understand correctly,
[tex]\frac{tan^4(x)}{4} + C = \frac{sec^4(x) - 1}{4} + C = \frac{sec^4(x)}{4} + C[/tex]
If that's wrong let me know please.
However, I don't get why I keep getting
[tex]\frac{tan^2(x)}{2}[/tex]
instead of
[tex]tan^2(x)[/tex]