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13 cards from this deck
Integration
∫xn dx=xn+1n+1+c\int x^n \, dx = \frac{x^{n+1}}{n+1} + c∫xndx=n+1xn+1+c
Accounts for lost constant (derivative of any constant is zero)
Definite integrals (give specific numerical answers)
ln∣x∣+c\ln|x| + cln∣x∣+c
1aln∣ax+b∣+c\frac{1}{a}\ln|ax+b| + ca1ln∣ax+b∣+c
1aeax+c\frac{1}{a}e^{ax} + ca1eax+c
−1acos(ax)+c-\frac{1}{a}\cos(ax) + c−a1cos(ax)+c
1asin(ax)+c\frac{1}{a}\sin(ax) + ca1sin(ax)+c
sin−1(xa)+c\sin^{-1}\left(\frac{x}{a}\right) + csin−1(ax)+c
1atan−1(xa)+c\frac{1}{a}\tan^{-1}\left(\frac{x}{a}\right) + ca1tan−1(ax)+c
F(b)−F(a)F(b) - F(a)F(b)−F(a) where F(x)F(x)F(x) is antiderivative
Differentiate result - should get original function back
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