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## Denebel 3 years ago Use the given trig identity to set up a u-substitution and then evaluate the indefinite integral.

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1. Denebel

|dw:1326790438109:dw|

2. FoolForMath

Yes, where are you stuck?

3. imperialist

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

4. Denebel

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

5. Denebel

Derivative of tan x is (sec x)^2

6. imperialist

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

7. imperialist

You will be pleasantly surprised!

8. FoolForMath

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

9. FoolForMath

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

10. FoolForMath

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. Denebel

Oh I see now. Thank you very much!

12. FoolForMath

Glad to help :)

13. imperialist

Likewise :)

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