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Practice: Long Division First

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Wize University Calculus 1 Textbook > Integrals

Antiderivatives of 1x\frac{1}{x}

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Evaluate ∫x3−x2−x−3x−2dx\displaystyle\int_{ }^{ }\frac{x^3-x^2-x-3}{x-2}dx
(a) x33+x22+x−ln⁡∣x−2∣+C\frac{x^3}{3}+\frac{x^2}{2}+x-\ln\left|x-2\right|+C (b) 12x2−3ln⁡∣x−2∣+C\frac12x^2-3\ln\left|x-2\right|+C (c) =x33+x22+x−12(x−2)2+C=\frac{x^3}{3}+\frac{x^2}{2}+x-\frac12(x-2)^2+C
More Antiderivatives of 1x\frac{1}{x} Questions:
Antiderivatives: Indefinite integrals
Evaluate the integral ∫1+1x+2x2+3x3dx\displaystyle\int_{ }^{ }1+\frac{1}{x}+\frac{2}{x^2}+\frac{3}{x^3}dx.
Antiderivatives: Indefinite integrals
Evaluate the integral ∫1+1x+2x2+3x3dx\displaystyle\int_{ }^{ }1+\frac{1}{x}+\frac{2}{x^2}+\frac{3}{x^3}dx.
Indefinite Integral
∫(x−2+x−1+1+x+x2)dx\displaystyle \int_{ }^{ }\left(x^{-2}+x^{-1}+1+x+x^2\right)dx
Practice: Long Division First
Q:\bf{Q:} Evaluate ∫x3−x2−x−3x−2dx\displaystyle\int_{ }^{ }\frac{x^3-x^2-x-3}{x-2}dx
Practice: Indefinite Integral
Evaluate the integral ∫x+1+1x+2x2dx\displaystyle\int_{ }^{ }x+1+\frac{1}{x}+\frac{2}{x^2}dx
Practice: Indefinite Integral
Evaluate the integral ∫1+1x+2x2+3x3dx\displaystyle\int_{ }^{ }1+\frac{1}{x}+\frac{2}{x^2}+\frac{3}{x^3}dx.
Antiderivatives
Evaluate the following indefinite integral
∫34−2x dx\displaystyle \int \frac{3}{4-2x} \ dx
Practice: Long Division First
Q:\bf{Q:} Evaluate ∫x3−x2−x−3x−2dx\displaystyle\int_{ }^{ }\frac{x^3-x^2-x-3}{x-2}dx
Antiderivatives: Indefinite integrals
Evaluate the integral ∫1+1x+2x2+3x3dx\displaystyle\int_{ }^{ }1+\frac{1}{x}+\frac{2}{x^2}+\frac{3}{x^3}dx.
Indefinite Integral
∫(x−2+x−1+1+x+x2)dx\displaystyle \int_{ }^{ }\left(x^{-2}+x^{-1}+1+x+x^2\right)dx