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Evaluate the following integrals.$$\int \frac{d \theta}{1+\sin \theta}$$

tan ? - sec ? + C

Calculus 1 / AB

Calculus 2 / BC

Chapter 8

Integration Techniques

Section 1

Basic Approaches

Integrals

Integration

Applications of Integration

Campbell University

Harvey Mudd College

Baylor University

University of Nottingham

Lectures

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So we have integral of D theta over one plus signed Fada. Well, when you look at this here, I immediately think Okay, let me multiply the top on bottom by one minus. Sign theater one minus. Sign fatal Here. So this will give us integral off. Uh, one minus sign. Fada over one, minus sine squared. Veda The Fed! Now we can split this. So that's 1/1 minus sign squared. Seita minus sign theater over one minus sine squared. So this is also remember one minus sine squared Theta is co sine squared things. So that's one over co signed squared theta. And this is minus sine theta over co signed Squared fada. Uh, so one over co sine squared is also second squared, Seda. Now I'm gonna doing integral here, So sign over Coastlines Quarter. That's also signed over co sign which it stand Data times one over co sign. So that's also seeking Fada. So now we have two standard into girls here. So the integral off seeking squared is tangent Fada minus the integral off tangent. Ah, seeking is just second plus c. So this is your final answer here

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