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Use a computer algebra system to evaluate the integral. Compare the answer with the result of using tables. If the answers are not the same, show that they are equivalent.

$ \displaystyle \int \frac{1}{\sqrt{1 + \sqrt[3]{x}}}\ dx $

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Calculus 2 / BC

Chapter 7

Techniques of Integration

Section 6

Integration Using Tables and Computer Algebra Systems

Integration Techniques

Campbell University

Oregon State University

Baylor 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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Use a computer algebra sy…

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Use a computer algebra sys…

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All right, This question wants us to use technology to find this anti derivative and then compare that to our tabular answer and make sure that they match So plugging this into a computer algebra system, this is very anti derivative. But then if we plug into a table, we get this. So these are the same answers you can see by inspection here. But the only difference is writing rational exponents in the computer algebra version. So just re rating the CS version. We get 6/5 times X to the 1/3 is just cube root of X minus four Again X to the 1/3 is Cuban X, and then only had to do was just expand this out and rewrite our rational exponents as cube roots. And now this answer completely matches what we're given in the tape. 6/5 negative. Four and six are coefficients here and 6/5 negative. Four and six are coefficients there. And of course, the order inside here doesn't matter, because addition is competitive

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