cu6l2-indefinite-integration-by-u-substitution

For more cool math videos visit my site at http://mathgotserved.com or http://youtube.com/mathsgotserved Good day students in this clip is going to be going over two examples on indefinite integration using the U substitution method to get started let's take a look at the formula for of integration using you substitution. So this is the formula. So basically the in definite integral of a composite function F of G of X multiplied by the derivative of the inner function G prime of X the X is equal to the integral of F of you the you okay this can only happen where you is equal to G of X and the use the differential the you is equal to G prime of X the X right to this is a general formula for integration are using you substitution method sonorities you substitution you going to have to functions a composite function in another function of the inner function of the composite function if it's derivative is the of multiple of the other function then you can use you substitution okay isolate take a look at an example that we can make use of that so the instructions are to evaluate the following evaluate the following so the first one is going to try out is the in definite integral of three X over the square root of X square plus three the X okay now I want to write this integral in this formula want to write it as a composite function can't another function okay so this three right here can factor that three out the constant multiple rule for integral so take that out I have the integral and the right of the composite function first this function right here is the rational function compose with the radical function and you have the quadratic function right there okay so we can write this as one over the square root of X square plus three times X the X now is going to do a test to see if I can be of use in take you substitution here is to the test and the side so this is a test to buy take of the inner function here and differentiated and see if you get the multiple of this function right here okay so let's take the inner function X square plus three hundred and differentiated so X group is three prime is equal to two X now this a multiple of this function right here absolutely so this is a good problem to use you substitution right so initially the steps to him in the substitution what here first you're going to do is going to pick the appropriate you write to the you is going to be making a function of the compose function what we do the test on which is X square plus three now the differentiate of if you differentiate this with the have the you the X is equal to two X if I multiply what sites by the X and the have the you equals two X the X try this is a different the derivative in differential for now him how I can make a clean substitution of X the X right but these two here so how the light of what I did to this equation second half X the X than it alone and I can substitute in this piece in order to accomplish that will have to divide both sides by two write so is going to have of the you over to the down with it is equal to X the X now we are ready to substitute okay so nice make a substitution is W three factor out of the integral of one over the square root of is at X square plus three is another become just you and then X the X is going to become the you over to write so we making your substitution using you substitution and then be to substitution happening the inner function we get substituted and the other function will get substituted also say have this integral right here right us this is a much easier integral to evaluate twenty go ahead and write it so you can see that it's in fact easy to evaluate the fact of these two out to the three to have three over to have the integral now one over the squared of you can written as one over used to the one half the you are using the reciprocal properties of an exponents I can write this the integrand as you today negative one half the you now compared this integral right here with this completely different this is much easier to evaluate of compared to of the original one right so is ahead and find the anti-derivative here we going to use the power rule vertical with the power rule is out apply

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