Calculus

# Integration of Rational Functions

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

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

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

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

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

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