1. ## integrate sex^3xtanx

integrate $sec^3x tanx$

i simplified the expression to this: $tanx sec^2x secx$

i don't know how to integrate the above expression though

2. Originally Posted by differentiate

integrate $sec^3x tanx$

i get something $tanx sec^2x secx$

i don't know how to proceed from here.

$\int(\sec^2{x}\sec{x}\tan{x})dx$

Now let $u=\sec{x}$ so that $du=\sec{x}\tan{x}dx$

And you have

$\int{u}^2du$

3. Originally Posted by differentiate

integrate $sec^3x tanx$

i get something $tanx sec^2x secx$

i don't know how to proceed from here.

Rewrite as

$\int{\sec^2{x}\sec{x}\tan{x}\,dx}$.

Let $u = \sec{x}$ so that $\frac{du}{dx} = \sec{x}\tan{x}$.

So the integral becomes

$\int{u^2\,\frac{du}{dx}\,dx}$

$= \int{u^2\,du}$

$= \frac{1}{3}u^3 + C$

$= \frac{1}{3}\sec^3{x} + C$.

4. Originally Posted by VonNemo19
$\int(\sec^3{x}\sec{x}\tan{x})dx$

Now let $u=\sec{x}$ so that $du=\sec{x}\tan{x}dx$

And you have

$\int{u}^3du$
Actually it's $\int{u^2\,du}$ because you need to rewrite it as $\int{\sec^2{x}\sec{x}\tan{x}\,dx}$.

5. Originally Posted by Prove It
Actually it's $\int{u^2\,du}$ because you need to rewrite it as $\int{\sec^2{x}\sec{x}\tan{x}\,dx}$.
Arggghhhhhhhhhhhh!!!!!!!!

I wrote that too, but then double checked.

It's time to go to bed.

6. Originally Posted by VonNemo19
Arggghhhhhhhhhhhh!!!!!!!!

I wrote that too, but then double checked.

It's time to go to bed.
Goodnight mate