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Given f(x)=∫2x+49x2+9x+14dx\displaystyle{f(x) = \int \frac{2x + 49}{x^2+9x+14} dx}f(x)=∫x2+9x+142x+49dx and f(0)=1,f(0) = 1,f(0)=1, find the function f(x).f(x).f(x).
Evaluate ∫184x3dx.\int_{1}^{8} \frac{4}{x^3} dx .∫18x34dx.
If f(x)=∫8x−9(x−3)(x−8)dx,\displaystyle{f(x) = \int \frac{8x-9}{(x-3)(x-8)} dx},f(x)=∫(x−3)(x−8)8x−9dx, what is f(5)−f(1)?f(5)-f(1)?f(5)−f(1)?
If f(x)=∫38x−219x2−2x−2edx\displaystyle{f(x)=\int \frac{38x-2}{19x^2-2x-2e}dx}f(x)=∫19x2−2x−2e38x−2dx and f(0)=1+ln2−ln19,f(0)=1+\ln 2-\ln 19,f(0)=1+ln2−ln19, what is the value of f(−e)?f(-e)?f(−e)?
Evaluate the indefinite integral ∫x2+17x−3dx.\int \frac{x^2+17}{x-3}dx.∫x−3x2+17dx. (Use CCC as the constant of integration.)
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