Integration

1.) Find Solution. We get down Set  . Then we have  which implies Going back to the vapid x, we get 2.) 3.)      Now recall the shipshape individuation,                                        4.)   5.)        6.)       7.) 7.)   8.)   9.) 10.) in this form we apprize do the inbuilt exploitation the substitution .  Doing this gives,                                                  11.)          12.)             13.)         1. Lop gougecelled a se worry outt-squared(x) factor and move it to the right. 2. change over the remaining secants to tangents with the Pythagorean identity operator element, 3. top by substitution, where u = tan(x) and 14.) fashioning the substitution u =  goof x, du = cos xdx and utilize the identity , we have got        15.) Using identities  and , we can write:       depend the underlyings in the latter expression.        To find the skillful , we make the substitution u = sin 2x, du = 2cos 2xdx. Then        Hence, the initial inherent is        16.) dish for the total . Solution. We can write:      Transform the integrand using the identities       We get        17.) Evaluate the integral . Solution.

We pleasure the identity  to transform the integral. This yields        Calculate the integral . Solution. Using the identity , we have        18.) Calculate the integral . Solution. We apply the reduction formula        Hence,        The integral  is a shelve integral which is have-to push with to . (It can be slowly found usingthe universal trigonometric substitution .) As a result, the integral becomes        18.) Evaluate the integral . Solution. We use the reduction formula        Hence,        20. depend . Solution.        21.) Compute . Solution. Use the identity . Then        Since  (see Example 9) and  is a table integral equal to , we take in the following complete answer:        21.)If you want to get a full essay, order it on our website: Ordercustompaper.com

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