Lecture 4 Chapter 7 Integrals Part 12

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Part - 12 Lecture - 4 Chapter 7 Integrals

“Whether you think you can or whether you think you can’t, you’re right!”
— Henry Ford —

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 \(\int\frac{px+q}{ax^2+bx+c}dx\),\(\int\frac{px+q}{\sqrt{ax^2+bx+c}}dx\),\(\int{(px+q)\sqrt{ax^2+bx+c}dx}\).

24. \( \int (3x-2)\sqrt{x^2+x+1}dx=(x^2+x+1)^\frac{3}{2}-\frac{7}{2}\left[\left(\frac{2x+1}{4}\right)\sqrt{x^2+x+1}+\frac{3}{8}log{\left|x+\frac{1}{2}+\sqrt{x^2+x+1}\right|}\right]+C \)

25. \( \int(x-5)\sqrt{x^2+x}dx=\frac{1}{3}(x^2+x)^\frac{3}{2}-\frac{11}{2}\left\{\frac{2x+1}{4}\sqrt{x^2+x}-\frac{1}{8}log{\left|\left(x+\frac{1}{2}\right)+\sqrt{x^2+x}\right|}\right\}+C \)

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