Calculus

Integration Techniques

Integration with Partial Fractions

         

If f(x)=4xx22x3dxf(x)=\int \frac{4x}{x^2-2x-3} dx and f(0)=15ln3,f(0)=15 \ln 3, what is the value of f(2)?f(2)?

If f(x)f(x) is a function such that f(x)=125x21f'(x)=\frac{1}{25x^2-1} and f(0)=7,f(0)=7, what is the value of f(1)?f(1)?

What is the indefinite integral x+2(x4)(x5)dx?\int \frac{x+2}{(x-4)(x-5)} dx? (Use CC for the constant of integration.)

If f(x)=12x2(x1)(x2+x+1)dxf(x)=\int \frac{12x^2}{(x-1)(x^2+x+1)} dx and f(0)=0,f(0)=0, what is the value of ef(9)4?\displaystyle{e^{\frac{f(9)}{4}}}?

If aa is a nonzero real number, what is 35x2a2dx? \int \frac{35}{x^2 - a^2} dx?

Details and assumptions

Use CC as the constant of integration.

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