Part 11 Lecture 4 Chapter 7 Integrals

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Part - 11 Lecture - 4 Chapter 7 Integrals

 Life is 10% what happens to us and 90% how we react to it. – Dennis P. Kimbro

Booklets/Notes/Assignments are typed here on this website and their PDFs will be made available soon.

INTEGRATION OF ALGEBRAIC FUNCTIONS

THIRD METHOD

We apply the third method only if the first two methods are failed.
\( px+q=A(ax^2+bx+c)^\prime+B\)
It can be applied if the question is in \(\int\frac{px+q}{ax^2+bx+c}dx\),\(\int\frac{px+q}{\sqrt{ax^2+bx+c}}dx\),\(\int{(px+q)\sqrt{ax^2+bx+c}dx}\).

20. \( \int\frac{x+2}{2x^2+6x+5}dx=\frac{1}{4}\log{|}2x^2+6x+5|+\frac{1}{2}{\tan}^{-1}{(}2x+3)+C \)

21. \( \int\frac{x+3}{5-4x-x^2}dx=-\sqrt{5-4x-x^2}+{\sin}^{-1}{\frac{x+2}{3}}+C \)

22. \( \int\frac{5x+3}{\sqrt{x^2+4x+10}}dx \)

23. \( \int\frac{6x+7}{\sqrt{(x-5)(x-4)}}dx=6\sqrt{x^2-9x+20}+34\log{\left|x-\frac{9}{2}+\sqrt{x^2-9x+20}\right|}+C \)

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