Hello

Originally Posted by

**Wonkihead** But I think $\displaystyle \frac{\sec{}^2x}{2}$ and $\displaystyle \frac{\tan{}^2x}{2}$ aren't equivalent, are they? What have I done wrong there?

Nothing is wrong in your work except that you forgot to add a constant to each anti-derivative. Using $\displaystyle \tan^2x+1=\sec^2x$, one can show that the two answers you've found are in fact similar :

$\displaystyle

\int{\tan{}x\sec{}^2x \,\mathrm{d}x}= \frac{\tan{}^2x}{2}+C=\frac{\sec^2x}{2}-\underbrace{\frac12+C}_{\text{constant}}=\frac{\se c^2x}{2}+C'

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