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Evaluate the integrals by making appropriate u-substitutions and applying the formulas reviewed in this section.$$\int e^{\tan x} \sec ^{2} x d x$$
Calculus 1 / AB
Calculus 2 / BC
Chapter 7
PRINCIPLES OF INTEGRAL EVALUATION
Section 1
An Overview of Integration Methods
Integrals
Integration
Integration Techniques
Trig Integrals
Trig Substitution
Missouri State University
Oregon State University
Harvey Mudd College
University of Michigan - Ann Arbor
Lectures
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In mathematics, a trigonom…
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In mathematics, trigonomet…
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Evaluate the integrals by …
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thigh. So in this question, we're going to be solving our indefinite integral using the method of you substitution. So we have the integral of e to the tan of X times thesis EQ and squared x d x. And so first thing we're going to do is we're gonna set Are you equal to the tan of X? And now we're gonna just take the derivative of both sides. So we're going to have d. U is equal to the tan of, uh, start at the Chan, vexed the seek and squared of X dx. And now we're going to divide both sides by the secret squared off X. We're gonna have d'you over the seek and squared acts is equal to D X. And from here we're just going to replace r 10 of acts with Are you and r d X with R D you over seek and squared of acts. So now we're going to have the equation that e to the U times, the seeking squared of x times d you over the seek and squared of X. So our sequins are just going to cross out and we're going to be left with the integral of e to the U. D you and e to the u It do you is just equal to e to the U plus c Ah, Now we're just going to substitute in for Are you and are you is equal to the tan of X So we're just going toe have e to the tan of x plus, see? And that is our final answer.
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