1. ## [SOLVED] integral

I have completely lost some sort of technique for this integral, could somebody help. thanks
$\displaystyle \int\frac{sin(x)}{cos^2(x)}dx$ I know the answer is $\displaystyle sec^2(x)$but I don't know how it was got?

2. Originally Posted by i_zz_y_ill
I have completely lost some sort of technique for this integral, could somebody help. thanks
$\displaystyle \int\frac{sin(x)}{cos^2(x)}dx$ I know the answer is $\displaystyle sec^2(x)$but I don't know how it was got?
$\displaystyle \frac{\sin{x}}{\cos^2{x}} = \frac{1}{\cos{x}} \cdot \frac{\sin{x}}{\cos{x}} = \sec{x} \cdot \tan{x}$

$\displaystyle \int \sec{x} \cdot \tan{x} \, dx = \sec{x} + C$

3. $\displaystyle -u=Cosx,\ du=Sinxdx$

$\displaystyle \int{\frac{du}{u^2}}=\int{u^{-2}du}=-u^{-1}+C=Secx+C$

4. Originally Posted by Archie Meade
$\displaystyle u=Cosx,\ du=\textcolor{red}{-}Sinxdx$

$\displaystyle \int\textcolor{red}{-}{\frac{du}{u^2}}=\int{\textcolor{red}{-}u^{-2}du}=u^{-1}+C=Secx+C$
...

5. nice one, Skeeter!
my brain always seems to shut down at this time of night!