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## Part - 16 Lecture - 4 Chapter 7 Integrals

“Success is walking from failure to failure with no loss of enthusiasm.” — **Winston Churchill**

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

__SPECIAL CASES FOR ALL THE THREE METHODS__

__SPECIAL CASES FOR ALL THE THREE METHODS__

34. \( \int\frac{2x}{(x^2+1)(x^2+3)}dx=\frac{1}{2}\log{\left|\frac{x^2+1}{x^2+3}\right|}+C \)

35. \( \int\frac{(3\sin{\theta}-2)\cos{\theta}}{5-{\cos}^2{\theta}-4\sin{\theta}}d\theta=3\log{|}2-\sin{\theta}|+\frac{4}{2-\sin{\theta}}+C \)

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

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