## Part - 11 Lecture - 4 Chapter 7 Integrals

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

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