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Evaluate the indefinite integral.$\int \frac{\sin (\ln x)}{x} d x$

$\cos (\ln x)+C$

Calculus 1 / AB

Calculus 2 / BC

Chapter 5

Integrals

Section 4

The Substitution Rule

Integration Techniques

Oregon State University

Harvey Mudd College

University of Nottingham

Boston College

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.

07:34

Evaluate the integral.…

02:38

Evaluate the following int…

03:06

Evaluate the integrals.

05:15

Find the indefinite integr…

07:02

Okay, so we're gonna let you is equal to ln of acts of the EU is equal to one over x t x applying substitution. We end up with the integral off the sign of you you which is equal to negative co sign of you, plus C back substituting. We end up with native co sign off ln of X plus c.

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