integrate sex^3xtanx

**differentiate** · January 23rd 2010, 11:15 PM

hi, please help me with a question:

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

thank you in advance

**VonNemo19** · January 23rd 2010, 11:19 PM

Originally Posted by differentiate

hi, please help me with a question:

integrate $sec^3x tanx$

i get something $tanx sec^2x secx$

i don't know how to proceed from here.

thank you in advance

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

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

And you have

$\int{u}^2du$

**Prove It** · January 23rd 2010, 11:23 PM

Originally Posted by differentiate

hi, please help me with a question:

integrate $sec^3x tanx$

i get something $tanx sec^2x secx$

i don't know how to proceed from here.

thank you in advance

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

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

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

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

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

**Prove It** · January 23rd 2010, 11:23 PM

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

**VonNemo19** · January 23rd 2010, 11:26 PM

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.

**Prove It** · January 23rd 2010, 11:35 PM

Originally Posted by VonNemo19

Arggghhhhhhhhhhhh!!!!!!!!

I wrote that too, but then double checked.

It's time to go to bed.

Goodnight mate

Thread: integrate sex^3xtanx

LinkBack

Thread Tools

Display

integrate sex^3xtanx

Similar Math Help Forum Discussions

Integrate 3 e^x

how to integrate this ??

Integrate

How to integrate x^x?

Integrate

Search Tags