Integration of Rational Functions


Given f(x)=2x+49x2+9x+14dx\displaystyle{f(x) = \int \frac{2x + 49}{x^2+9x+14} dx} and f(0)=1,f(0) = 1, find the function f(x).f(x).

Evaluate 184x3dx.\int_{1}^{8} \frac{4}{x^3} dx .

If f(x)=8x9(x3)(x8)dx,\displaystyle{f(x) = \int \frac{8x-9}{(x-3)(x-8)} dx}, what is f(5)f(1)?f(5)-f(1)?

If f(x)=38x219x22x2edx\displaystyle{f(x)=\int \frac{38x-2}{19x^2-2x-2e}dx} and f(0)=1+ln2ln19,f(0)=1+\ln 2-\ln 19, what is the value of f(e)?f(-e)?

Evaluate the indefinite integral x2+17x3dx.\int \frac{x^2+17}{x-3}dx. (Use CC as the constant of integration.)


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