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13 cards from this deck
xn+1n+1+c\frac{x^{n+1}}{n+1} + cn+1xn+1+c
lnx+c\ln x + clnx+c
1aln(ax+b)+c\frac{1}{a}\ln(ax + b) + ca1ln(ax+b)+c
∫abf(x)dx=F(b)−F(a)\int_a^b f(x)dx = F(b) - F(a)∫abf(x)dx=F(b)−F(a)
∫u dv=uv−∫v du\int u \, dv = uv - \int v \, du∫udv=uv−∫vdu
Choosing uuu in integration by parts
v=dsdtv = \frac{ds}{dt}v=dtds (first derivative of distance)
a=dvdta = \frac{dv}{dt}a=dtdv (first derivative of velocity)
W=∫abF(x)dxW = \int_a^b F(x)dxW=∫abF(x)dx
Arbitrary constants
Initial conditions to find specific constants
dydx\frac{dy}{dx}dxdy, then d2ydx2=vdvdy\frac{d^2y}{dx^2} = v\frac{dv}{dy}dx2d2y=vdydv
Differentiation of constant gives zero
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