## anonymous 4 years ago Use the given trig identity to set up a u-substitution and then evaluate the indefinite integral.

1. anonymous

|dw:1326790438109:dw|

2. anonymous

Yes, where are you stuck?

3. anonymous

Hint: what is the derivative of tan(x)?

4. anonymous

How to start? Can I do this ? |dw:1326790556349:dw|

5. anonymous

Derivative of tan x is (sec x)^2

6. anonymous

Yes, so try only breaking one of the (sec x)^2 into 1+(tan x)^2

7. anonymous

You will be pleasantly surprised!

8. anonymous

$\int \sec^4 x \space dx = \int (1+\tan^2 x) \sec^2 x \space dx$

9. anonymous

Now put $$\tan x = z \implies \sec^2 x dx = dz$$

10. anonymous

So, $\int (1+\tan^2 x) \sec^2 x \space dx = \int (1+z^2) dz$ I am sure you can proceed after this.

11. anonymous

Oh I see now. Thank you very much!

12. anonymous