if sec^2 x - tan^2 x =1 is sec^4 x - tan^4 x =1 or any other bigger even power will also be like this?
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Originally Posted by ameerulislam if sec^2 x - tan^2 x =1 is sec^4 x - tan^4 x =1 or any other bigger even power will also be like this? NO! That is true because $\tan^2(x)=\sec^2(x)-1$.
Originally Posted by Plato NO! That is true because $\tan^2(x)=\sec^2(x)-1$. ok, so is there any work around like $(\tan^2(x))^2=(\sec^2(x))^2-1$ sorry if I sound stupid..
my original problem was $\int \frac{(3x^3)}{\sqrt {x^2-25}} dx$ used trig substitution technique to substitute $x, x=a sec^2x$
Originally Posted by ameerulislam my original problem was $\int \frac{(3x^3)}{\sqrt {x^2-25}} dx$ used trig substitution technique to substitute $x, x=a sec^2x$ Use $x=5 sec(u)$ then $dx=5\tan(u)\sec(u)du$ Notice that $\sqrt{25\sec^2(u)-25}=5\sqrt{\sec^2(u)-1}$ This should a lesson: Post the actual question first.
Last edited by Plato; Mar 8th 2014 at 12:16 PM.
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