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Integrate each of the given functions.$$\int \frac{1-\cot ^{2} x}{\cos ^{2} x} d x$$
$\tan x+\cot x+C$
Calculus 1 / AB
Chapter 28
Methods of Integration
Section 4
Basic Trigonometric Forms
Integrals
Harvey Mudd College
University of Michigan - Ann Arbor
Boston College
Lectures
05:53
In mathematics, an indefin…
40:35
In mathematics, integratio…
00:54
Find each integral.$$\…
03:53
Evaluate the following int…
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01:19
Evaluate the indicated int…
Evaluate the integral.…
01:05
Evaluate the integrals.
01:23
Evaluate the integrals…
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03:52
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03:37
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Integrals with $\sin ^{2} …
00:21
02:26
Evaluate the integral.
03:27
Calculate the integral.
00:42
Now evaluate the following…
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01:47
we want to integrate the given expression which is the integral of one minus coach agents Weird X over cosine squared X dx. Or as I've written by distributing the denominator so you can't squared x minus cozy. Can't squared x dx to solve this problem, we need to rely on methods of integration. Previously we learned about the power rule, log rule and exponential rule for this problem. We need to use geometric engine rules To use talking to girls properly. We have to match the form of are integral to the form of one through 10. So since we actually have the sum of two trig functions you can't square minus coast. You can't squared We're going to use to two of these rules. Specifically Rules three and four. So using Rules three and four, we note that you and D. You are both X&DX and both problems. So it's quite simple integral. Thus we apply rules three solutions can X plus C and rule for solution negative co tan you plus C, from which we obtain our solution for this problem are integral, is Can express go Tangent X. Policy or the negative in our integral and in the solution to four cancel.
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