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10 cards from this deck
โซxndx=xn+1n+1+C\int x^n dx = \frac{x^{n+1}}{n+1} + Cโซxndx=n+1xn+1โ+C
โซxโ1dx=lnโกโฃxโฃ+C\int x^{-1} dx = \ln|x| + Cโซxโ1dx=lnโฃxโฃ+C
When n=โ1n = -1n=โ1, because it causes division by zero.
โซx2dx=x33+C\int x^2 dx = \frac{x^3}{3} + Cโซx2dx=3x3โ+C
โซxโ3dx=โ12x2+C\int x^{-3} dx = -\frac{1}{2x^2} + Cโซxโ3dx=โ2x21โ+C, for xโ 0x \neq 0x๎ =0
Evaluate the antiderivative at limits and subtract.
โซabxndx=xn+1n+1โฃab\int_a^b x^n dx = \frac{x^{n+1}}{n+1}\bigg|_a^bโซabโxndx=n+1xn+1โโabโ
CCC is the constant of integration.
โซexpressionโdx\int \text{expression} \, dxโซexpressiondx, where dxdxdx is the variable.
โซ(5x1/2+2)dx=103x3/2+2x+C\int(5x^{1/2} + 2) dx = \frac{10}{3}x^{3/2} + 2x + Cโซ(5x1/2+2)dx=310โx3/2+2x+C
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