MHB Simplifying the Integral of 20 sec^3(x) dx using Trigonometric Identities

[dexstarr]

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 can't seem to cancel anything out.

 

[SuperSonic4]

Re: Integral of 20 sec^3(x)dx

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 can't seem to cancel anything out.

$$20 \int \frac{1}{\cos^3(x)}$$

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

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

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

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

 

[topsquark]

Re: Integral of 20 sec^3(x)dx

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

Coooool! I've never seen that method.

-Dan