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Find the general indefinite integral.

$ \displaystyle \int \frac{\sin 2x}{\sin x}\, dx $

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00:31

Frank Lin

00:49

Amrita Bhasin

Calculus 1 / AB

Chapter 5

Integrals

Section 4

Indefinite Integrals and the Net Change Theorem

Integration

Missouri State University

Baylor University

University of Michigan - Ann Arbor

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.

00:20

Find the general indefinit…

00:46

01:59

02:14

Evaluate the integral.

00:29

Find the indefinite integr…

00:19

All right. All you need is a trig identity and you might need a google trig identities if you're not very good at them To do this problem sign of two x over sine of X. So what I would do is just rewrite this and there's a double angle formulas. There's only one of them. So you can't be that lost. Once you find it a double angle for sign of to access to sign of X times Cosine of X. Now this sine of X on the bottom is still there. And the reason why that should be helpful is because then you could cancel out that sine of X. And uh you can think about or you could just know memorize the anti derivative of co sign a sign. I usually just think about what derivative would give me co sign and that would be positive sign. And then you just gotta remember about your plus C. Um So I think I've explained everything fully. Just a reminder that the derivative of this needs to equal this, which is equal to that. Uh And it is and you need the plus Eek is the derivative of a constant zero. And we're not gonna write plus zero up here, which is why we have that for every answer.

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