Calculus 2: True False (Partial Fraction) and Divergence of Integral

Posted on September 25, 2023 by Sumant Sumant

The partial fraction decomposition of the rational function \dfrac{x(x^2+1)}{x^2-9} is \dfrac{A}{x-3}+\dfrac{B}{x+3} for some constants A and B.

The following improper integral diverges \int_{1}^{\infty}\dfrac{2-\sin^{4}x}{x}dx

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