i'm confused on which item should be my u and which should be my du, i've tried a few values on all problems but I feel my answer is wrong and that I'm overlooking something, if you could please help I would be eternally grateful!
Use U substitution to solve the following:
a)anti derivative of cos(x)/sin^2(x) dx top valuei/2 bottom value: pi/4
b) (4(tan^-1(x))^2)/(1+x^2) dx top value: 1 bottom value: -1
c) 5x(3x^2 - 12)^9 dx top value: 4 bottom value: 0
If then so . Substitute these values into the original integral to obtain . The limits of the integral are determined by the values of at the corresponding values of .
This isn't a product. This can be evaluated using the basic formula:
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Secondly, there isn't a product rule for integration. There's only a sum and diffference rule. For product and quotients you have to deal with on a case-by-case basis. Sometimes you need to use either the substitution rule, integration by parts, partial fractions, etc. For example:
We know that , so if we use then . This means that we can substitute into the original equation, canceling out the and leaving only which is equal to .
Now we have
Therefore: