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Evaluate the integral.$$\int \frac{1}{(x+a)(x+b)} d x$$

$\frac{1}{b-a} \ln \left|\frac{x+a}{x+b}\right|+C$

Calculus 1 / AB

Calculus 2 / BC

Chapter 5

Integrals

Section 6

Partial Fractions

Integration Techniques

Campbell University

Oregon State University

University of Michigan - Ann Arbor

University of Nottingham

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

07:51

Evaluate the integral.

02:12

Evaluate the integral.…

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00:53

Evaluate the indefinite in…

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Okay, so if we decompose it into partial fractions, we end up with a over X plus small a plus V over X plus small. Be multiplying both sides by the least common denominator. We end up with a multiplied by X plus V plus be multiplied by X plus a so setting X is equal to native A. We end up with a is equal to one over B minus eight on setting X is equal to negative. B we end up with B is equal to one over a minus b So putting this back in we end up with won over B minus a times the integral off one over X plus a minus one over X plus b. So using the law, properties get up with one over B minus a times ln of the absolute value off X plus a divided by explosive speed plus C.

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