Hello, Tom from everystepcalculus.com and everystepphysics.com, I’m going to show you how to do this integration problem that a student asked for help with Yahoo and so I’ll show you how my programs work on this. Index 8 to get to my menu I’m already at U substitution, I’ll show you why it’s used substitution in a little bit. We’re gonna enter the function you have to press alpha first before you enter things in these entry lines here in my program. So, I’m going to press alpha the problem is one / what put the left parenthesis in for the divisor and second and then we get the square root sign of 2 times X – X2 and then cap it off with the 2 parentheses. Press Enter and looks pretty good here we’re gonna rewrite it, bringing the X2 – 2X in the proper form because we’re going to complete the square. Something you’re probably an expert on but not me so I wanted to show you how to do that and we’re going to complete the square by taking the half of the middle term here squaring it. This is – 1, – 12 and anytime in mathematics when you add something to a formula or function you have to take away the same thing to make it easy. You can’t change things just for no reason so we subtract the – 12 here also. Okay, this sets up the identity the integral of one divided by the square root of a squared minus U2, DU is equal to the arc sine of U over A plus C. So, U is X – 2 and A = 1 here’s the U2 or use substitution area. So, pathetic calculus you know and so we add the U and the A and we come up with the answer here. Arc sine of X – 2 plus C isn’t this wonderful.
Now, notice that the any time you do the arc sine you’re finding the angle in trigonometry okay. So, now you’ve found the angle and you still have to add some arbitrary C there’s ten million answers to this problem unless somebody comes up with a letter C okay. So, again when you find these answers notice how nonsensical they are and how useless they are the answers which calculus does totally it suggested hundreds of little puzzles that professors have dreamed up to solve here and they solve nothing. They just come up with answers and we get so involved when we’re trying to pass tests that we get involved with this stuff and say oh that’s good. We just got the answer here and the answer is generally is complicated or more complicated than the original function but that’s calculus okay. Now, you can go to my site buy my programs for $40, best $40 you’ll ever spend and you already can study this stuff for hours like I have to find the steps to do it. Find the best way of doing these problems and you know you can buy my programs and pass calculus and cut down on your study time and everything else okay. So, think about that but have a good one okay.