# Math Help - integration of x.secx.tanx

1. ## integration of x.secx.tanx

how would you integrate x.secx.tanx dx??
thanks for any help

2. $\int x\sec{x}\tan{x}~dx = \int x(\sec{x})'~dx = x\sec{x} - \int \sec{x}~dx$

It can be easily shown that $\int \sec{x}~dx = \ln|\sec{x}+\tan{x}|$ by multiplying the integral expression with $\frac{\sec{x}+\tan{x}}{\sec{x}+\tan{x}}$

3. ## tanx

what happened to the tanx???

4. Recall that:

$\frac{d}{dx} \sec{x}= (\sec{x})' = \sec{x}\tan{x}$

I wrote $\sec{x}\tan{x}$ in an equivalent form $(\sec{x})'$ as it is easier and faster to see what u and v when using integration by parts.

5. $\int x\cdot sec(x)tan(x)dx$

Use parts, Let $u=x, \;\ dv=sec(x)tan(x)dx, \;\ du=dx, \;\ v=sec(x)$

We get:

$xsec(x)-\int sec(x)dx$

Now, it's easier, huh?.

6. ## thanks

thanks to both of you i was having trouble seeing that one