## anonymous 3 years ago This exercise is in a section about using trig substitution to integrate. I can use trig sub, but I'm just not seeing what initial substitution to use so I can apply trig sub. Can anyone give me a hint? I don't need (don't want) it solve to the end. At least not yet.

1. anonymous

See attached

2. anonymous

|dw:1342935015183:dw|

3. anonymous

woops cos theta/4 = 1/ hypotenuse, not just the hypotenuse

4. anonymous

just a guess with what is out there

5. anonymous

|dw:1342935652408:dw| actually this looks better

6. anonymous

then |dw:1342935809458:dw|

7. anonymous

hint: use trig identity $\sec^{2} = 1+\tan^{2}$ Factor out the 16 from radical in denominator $\sqrt{16+x^{6}} = \sqrt{16}\sqrt{1+\frac{x^{6}}{16}}$ Now make the substitution $x^{6} = 16\tan^{2}$ hope that helps