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Evaluate the integral.

$ \displaystyle \int \tan x \sec^3 x dx $

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Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 2

Trigonometric Integrals

Integration Techniques

Missouri State University

Campbell University

Harvey Mudd College

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 indefinite in…

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Evaluate the integrals.

This problem is from Chapter seven section to problem number twenty one in the book Calculus Early Transcendental Sze eighth Edition by James Door Here we have a indefinite a roll of tangent times he can't cube. So here, let's re write it Seeking cute Becks as c can't squared of eggs Time seeking a Vicks and let's sleep Tangent avec says it is The reason for doing this is because if we grouped these last two terms here to suggest that we should try a new substitution, you equal See Kanna Becks So that do you is seeking a bucks tangent of X t X, which is exactly what we have in the end A gram. So after using this u substitution R interval simply becomes you square, Do you? Now we can use the power rule to evaluate this integral you cubed over three plus Don't forget our constant of integration seat. And now we could come back to our Are you substitution to replace you with seeking of X? So we have He can't keep the bugs over three plus he and there's our answer. Thank you

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