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Evaluate the indefinite integral.

$ \displaystyle \int \cot x \, dx $

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01:14

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 5

The Substitution Rule

Integration

Campbell University

Oregon State University

Harvey Mudd College

Boston College

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

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We're looking at the integral of Coach engine axe d x We know that cotija axes cosign x o ver sine x, which means now we're looking at the integral of coastline acts over sign acts de axe. Okay. What this means now is that if you is sign acts, then de axe is d'you over co sign X Once we've taken the derivative of science, which is co sacks which means now we know the integral is won over you. Do you which substituting us? Sign X. We end up with our final solution of natural log of sign axe plus C.

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