1. ## integrate sex^3xtanx

integrate $\displaystyle sec^3x tanx$

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

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

2. Originally Posted by differentiate

integrate $\displaystyle sec^3x tanx$

i get something $\displaystyle tanx sec^2x secx$

i don't know how to proceed from here.

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

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

And you have

$\displaystyle \int{u}^2du$

3. Originally Posted by differentiate

integrate $\displaystyle sec^3x tanx$

i get something $\displaystyle tanx sec^2x secx$

i don't know how to proceed from here.

Rewrite as

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

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

So the integral becomes

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

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

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

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

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

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

And you have

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

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

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### Sex tam3x

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