Integration of inverse trig functions

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SUMMARY

The discussion centers on the integration of inverse trigonometric functions, specifically addressing a confusion regarding the transition from 1/2 to 1/4 in the integration process. The participant clarifies that the correct interpretation involves recognizing that the factor of 1/2 should not be canceled but rather understood in the context of the substitution method where du = 2dx. The participant concludes that the book's presentation may have misleadingly simplified the expression, leading to the appearance of 1/4 instead of the accurate 1/2.

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bobsmith76
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This is an integration of an inverse trig function.
I don't see how they go from 1/2 to 1/4. I understand how they get the 1/2, du = 2dx, divide both sides by 2, but where does the 1/4 come from?
 
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Ok, I've done some more research and looks like if anything the 1/2 should just be canceled out because you're supposed to put du in the numerator, which is 2 and 2 times .5 = 1.
 
never mind, it looks like 1/4 but it's really 1/2. the book cut off the top part of 1/2 to make it look like 1/4. i found some guy on youtube doing the exact same problem.
 

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