Question

integral of x^2 / (9sqrt3 * sec^5 x)

Answer 1

\[\int\limits_{}^{}\frac{ x^2 }{ 9\sqrt{3} \sec^5x }dx\] is this what you have?

Answer 2

yes

Answer 3

I'm going to assume you do. Okay so the integrand (what's inside the integral can rewritten as:
\[\frac{ 1 }{ 9\sqrt{3} }\frac{ x^2 }{ \sec^5x }\] and remember when doing integrals when you have a product like above where one is a constant (a number that doesn't involve variables) you can put it in front of the integral so we have:
\[\frac{ 1 }{ 9\sqrt{3} }\int\limits_{}^{}\frac{ x^2 }{ \sec^5x }dx\]

Answer 4

Ok, I get that.

Answer 5

What's next?

Answer 6

Next we play around with the sec^5x what can we rewrite it as?

Answer 7

(sec^2 x)^2 (secx)?

Answer 8

or, turn it into cos?

Answer 9

So do you think you can do
\[\int\limits_{}^{}x^2\cos^5x dx\]

Answer 10

since secx=1/cosx

Answer 11

Then it's x^2 (1-sin^2 x)^2 (cos x)?

Answer 12

that second factor needs to be to the power of 4

Answer 13

I have to go but here is a link
http://integrals.wolfram.com/index.jsp?expr=%28x%5E2%29*%28cosx%29%5E5&random=false

Answer 14

Yeah That Too Helped me^

Answer 15

@goformit100 I'm not sure where to go from there. Can you help me?

Answer 16

use By parts .. write cos^5(x) as (1-sin^2x)^2 cos(x) to evaluate integral of cos^5(x)

Answer 17

I got sinx -(2sin^3 x)/3 + sin^5/5 for the integral of cos^5

Answer 18

use integration by parts again to get rid of x

Answer 19

I think I'm doing it wrong. I'm about to do integration by parts 3 times.

Answer 20

you deal with that constant .. i'll write the outline.