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Evaluate the integrals$$\int \sec ^{4} x \tan ^{2} x d x$$

Calculus 1 / AB

Calculus 2 / BC

Chapter 8

Techniques of Integration

Section 2

Trigonometric Integrals

Integrals

Integration

Integration Techniques

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Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

00:31

Evaluate the integrals.

00:53

Evaluate the integrals…

01:21

01:31

Evaluate the integral.…

00:35

00:50

10:55

05:34

11:12

02:18

Evaluate the integral.

section eight dot to number 38. So we're looking for the indefinite, Integral. Ah, the secret to the fourth of X changes squared of x d x. The key with many of these is to get our powers in terms of squares. So if I write, this is seeking squared of eggs seeking squared If x changes squared of x t x I know the seeking squared is one plus the tension squared So this is the integral of the secret squared of X one plus changes squared of X times attention's great of X, d x and the puzzle with many into grows If I can look at a function and his derivative appearing, I can usually make a U substitution. Well, I do see that here, if you is equal to the tangent of X then I know that Do you iss seeking squared of x d x So this becomes the integral of one plus u squared times you squared to you which is the interval of you to the fourth plus u squared Do you which is you to the fifth over five plus you cubed over three plus a constant of integration and we know you is equal to the change it of X. Therefore, this answer is just 1/5 attention to the fifth of X plus 1/3 tension cubed of X plus a constant of integration.

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