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Antiderivatives

This is the opposite of the derivative - and it's an integral part of Calculus. It's uses range from basic integrals to differential equations, with applications in Physics, Chemistry, and Economics.

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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