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Problem

Evaluate the integral. $$ \int \frac{\cos \theta}…
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Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 Problem 21 Problem 22 Problem 23 Problem 24 Problem 25 Problem 26 Problem 27 Problem 28 Problem 29 Problem 30 Problem 31 Problem 32 Problem 33 Problem 34 Problem 35 Problem 36 Problem 37 Problem 38 Problem 39 Problem 40 Problem 41 Problem 42 Problem 43 Problem 44 Problem 45 Problem 46 Problem 47 Problem 48 Problem 49 Problem 50 Problem 51 Problem 52 Problem 53 Problem 54

Problem 19 Easy Difficulty

Evaluate the integral.
$$
\int e^{x} \sqrt{1-e^{2 x}} d x
$$

Answer

$\frac{1}{2} \sin ^{-1}\left(e^{x}\right)+\frac{1}{2} e^{x} \sqrt{1-e^{2 x}}+C$

Related Courses

Calculus 1 / AB

Calculus 2 / BC
Calculus Early Transcendentals

Chapter 7

PRINCIPLES OF INTEGRAL EVALUATION

Section 4

Trigonometric Substitutions

Related Topics

Integrals

Integration

Integration Techniques

Trig Integrals

Trig Substitution

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Problem 13
Problem 14
Problem 15
Problem 16
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Problem 18
Problem 19
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Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
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Problem 31
Problem 32
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Problem 35
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Problem 48
Problem 49
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Problem 51
Problem 52
Problem 53
Problem 54

Video Transcript

we want to integrate this function, we will be using substitution method. Let you equals to eat about X Then we know that you square is actually eat about two weeks When we differentiate, you will be differentiating eat about X which will be itself And in Vieques So we have either Ball X, you and Kiesler So let me write it in properly. I have this and I have either bought x dx you so I can replace. Eat above, do extra you square and it'll bar next. Yes, we do. You surges is what I have one minus you square square roots here. And do you We know that integrating this we will get sine inverse new plus See us sees a constant Now we can replace the You bet we eat about extra final answer is signing verse Eat about X plus e

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Howard Anton, Irl Bivens, Stephen Davis

Calculus Early Transcendentals

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