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10 cards from this deck
∫xndx=xn+1n+1+C\int x^n dx = \frac{x^{n+1}}{n+1} + C∫xndx=n+1xn+1+C
∫x−1dx=ln∣x∣+C\int x^{-1} dx = \ln|x| + C∫x−1dx=ln∣x∣+C
When n=−1n = -1n=−1, because it causes division by zero.
∫x2dx=x33+C\int x^2 dx = \frac{x^3}{3} + C∫x2dx=3x3+C
∫x−3dx=−12x2+C\int x^{-3} dx = -\frac{1}{2x^2} + C∫x−3dx=−2x21+C, for x≠0x \neq 0x=0
Evaluate the antiderivative at limits and subtract.
∫abxndx=xn+1n+1∣ab\int_a^b x^n dx = \frac{x^{n+1}}{n+1}\bigg|_a^b∫abxndx=n+1xn+1ab
CCC is the constant of integration.
∫expression dx\int \text{expression} \, dx∫expressiondx, where dxdxdx is the variable.
∫(5x1/2+2)dx=103x3/2+2x+C\int(5x^{1/2} + 2) dx = \frac{10}{3}x^{3/2} + 2x + C∫(5x1/2+2)dx=310x3/2+2x+C
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