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Evaluate the integral.

$ \displaystyle \int \tan^2 x dx $

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$\tan (x)-x+c$

Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 2

Trigonometric Integrals

Integration Techniques

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

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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00:32

Evaluate the integral.…

09:32

this problem is from Chapter seven section to problem number twenty three in the book Calculus Early. Transcendental lt's a Tradition by James Store. Here we have a indefinite integral of tangent squared of X. So here we can use the fact that one of our protection identities is tan square of eggs plus one equals sequence quarterbacks. So solving this for Tan's flared we have ten Tan squared is seeking squared minus one. So using this fact, we have in a girl seeking squared X minus one, and we can evaluate these integral separately. The integral of seek and square is simply tangent of X, and the integral of one is just X, and we also have our constant of integration, see, And there's our final answer.

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