diff. trig integral

**saiyanmx89** · February 24th 2009, 04:55 PM

$\int tan^3(2t)sec^3(2t)dt = \int tan^2(2t)sec^2(2t)sec(2t)tan(2t)dt $

$u = sec2t$
$du = sec(2t)tan(2t)dt$

$\int (tan^2(2t)u^2)du$

Am I going in the right direction?

**Reckoner** · February 24th 2009, 05:17 PM

Originally Posted by saiyanmx89

$\int tan^3(2t)sec^3(2t)dt = \int tan^2(2t)sec^2(2t)sec(2t)tan(2t)dt $

Try this:

$\int\tan^32t\sec^32t\,dt$

$=\int\tan^22t\tan2t\sec^32t\,dt$

$=\int\left(\sec^22t-1\right)\tan2t\sec^32t\,dt$

$=\int\tan2t\sec^52t\,dt-\int\tan2t\sec^32t\,dt$

$=\int(\sec2t\tan2t)\sec^42t\,dt-\int(\sec2t\tan2t)\sec^22t\,dt$

Now do $u=\sec2t.$

**Scott H** · February 24th 2009, 05:19 PM

You are going in the right direction, only

$ \begin{aligned} u&=\sec 2t \\ du&=2 \sec 2t \tan 2t\,dt. \end{aligned} $

Now you can use the fact that $\tan^2 t+1=\sec^2 t$ .

**skeeter** · February 24th 2009, 05:25 PM

$\int \tan^3(2t)\sec^3(2t) \, dt$

$\int \tan^2(2t)\sec^2(2t)\sec(2t)\tan(2t) \, dt$

$\int [\sec^2(2t) - 1]\sec^2(2t)\sec(2t)\tan(2t) \, dt$

$\int [\sec^4(2t) - \sec^2(2t)]\sec(2t)\tan(2t) \, dt$

$u = \sec(2t)$

$du = 2\sec(2t)\tan(2t) \, dt$

$\frac{1}{2} \int [\sec^4(2t) - \sec^2(2t)] \cdot 2\sec(2t)\tan(2t) \, dt$

$\frac{1}{2} \int u^4 - u^2 \, du$

**saiyanmx89** · February 24th 2009, 05:32 PM

Originally Posted by Reckoner

Try this:

$\int\tan^32t\sec^32t\,dt$

$=\int\tan^22t\tan2t\sec^32t\,dt$

$=\int\left(\sec^22t-1\right)\tan2t\sec^32t\,dt$

$=\int\tan2t\sec^52t\,dt-\int\tan2t\sec^32t\,dt$

$=\int(\sec2t\tan2t)\sec^42t\,dt-\int(\sec2t\tan2t)\sec^22t\,dt$

Now do $u=\sec2t.$

what would du =?

**Reckoner** · February 24th 2009, 05:37 PM

Originally Posted by saiyanmx89

what would du =?

You should learn and know the derivatives of all six of the basic trigonometric functions.

$\frac d{dx}[\sec x]=\sec x\tan x$

Thread: diff. trig integral

LinkBack

Thread Tools

Display

diff. trig integral

Similar Math Help Forum Discussions

Can someone help me please... (Integral/Diff. Calculus)

trig integral

Trig Integral help

inverse trig integration:two methods=two diff ans HELP!!

Implicit diff first or inverse trig first?

Search Tags