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Evaluate the integral.

$ \displaystyle \int (\tan^2 x + \tan^4 x) dx $

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Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 2

Trigonometric Integrals

Integration Techniques

Campbell University

Oregon State University

Idaho State University

Lectures

01:53

In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative. The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis. The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.

27:53

In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.

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Evaluate the integral.…

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Evaluate the integrals.

01:54

Evaluate the following int…

this problem is from Chapter seven section to problem number twenty four in the book Calculus Early. Transcendental. Lt's a tradition. My James store. Here we have an indefinite animal of Tangent Square plus tensions of the four power. So one way to proceed here suggest factor out its hand square. If we do that, we pull out its hand squared and we're left over with one plus ten square of X. And now we can apply our path. Agron Identities too. Rewrite one plus tan squared is sequence where at this point, we can apply u sub Let's take you two be tangent of X so that do you is sick and scared of x e x So here the sea cans Word of the X That's our do you in this tan square of X, this is Wilby. You squared so that our interval becomes you. Swear to you. Okay, we can use the power all to evaluate this General factions becomes you cued over three plus e and then we could These are useless institution toe back, substitute from you back in terms of X. So us you cue becomes Tan Cube X. We have to divide that by three and then we are see and there's our answer

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