9 lines
398 B
Markdown
9 lines
398 B
Markdown
# Obliczyć całki z funkcji wymiernych.
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## 1
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$$\int\frac{x+2}{x-3}dx=\int\frac{x-3}{x-3}+\frac{5}{x-3}dx=\int1+\frac{5}{x-3}dx=x+5\ln|x-3|+C$$
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## 2
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$$\int\frac{2x+3}{2x+5}dx=\int1+\frac{-2}{2x+5}dx=x-\log(x+\frac{5}{2})+C$$
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## 3
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$$\int\frac{x^{2}dx}{x-1}=\int x^{2}\cdot\frac{1}{x-1}dx$$
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## 4
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$$\int\frac{x^{3}+x+1}{x-1}dx=\int\frac{x(x^2+1)+1}{x-1}dx=\int\frac{x(x^{2}+1)}{x-1}+\frac{1}{x-1}dx$$ |