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- Thread starter dexstarr
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- Thread starter
- #1

- Mar 1, 2012

- 249

\(\displaystyle 20 \int \frac{1}{\cos^3(x)}\)I'm having a hard time breaking this down using tri identities.

} = integral sign

20}sec^3(x) dx

20}sec^2(x) * sec(x) dx

20}[tan^2(x)-1] * sec(x) dx

after this I'm stuck. I tried letting u = tan(x) or sec(x) but i cant seem to cancel anything out.

Multiply by \(\displaystyle \dfrac{\cos(x)}{\cos(x)}\)

\(\displaystyle 20 \int \frac{\cos(x)}{\cos^4(x)}\)

\(\displaystyle 20 \int \frac{\cos(x)}{(1-\sin^2(x))^2}\)

Now use \(\displaystyle u = \sin(x)\)

- Aug 30, 2012

- 1,123

Coooool! I've never seen that method.Multiply by \(\displaystyle \dfrac{\cos(x)}{\cos(x)}\)

-Dan