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Evaluate the indefinite integral.$\int \frac{d t}{\cos ^{2} t \sqrt{1+\tan t}}$
$2 \sqrt{1+\tan t}+C$
Calculus 1 / AB
Calculus 2 / BC
Chapter 5
Integrals
Section 4
The Substitution Rule
Integration Techniques
Harvey Mudd College
University of Michigan - Ann Arbor
University of Nottingham
Lectures
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Evaluate the integrals.
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03:01
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05:17
Evaluate the integral.
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01:42
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04:27
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03:13
Evaluate the integrals…
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00:52
Evaluate the definite inte…
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01:34
Okay, So if we rewrite the identical integral and then you see, I didn't see that one over coz I is equal to the seacat 50 We can get the integral off seek end squared of t t t divided by the square root of one plus the tangent of tea So we're gonna let you is equal to one plus the tangent of teeth so that D u is equal to see Ken squared of t t t. So we end with Theo integral of you to the power of negative 1/2 to you which is just equal to you to the power off 1/2 multiplied by two, which is two times the square root of you plus c back substituting who is equal to one plus the tangent if t we end up with two times the square root of one plus the tangent of tea plus seat
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