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15 cards from this deck
xn+1n+1+c\frac{x^{n+1}}{n+1} + cn+1xn+1+c
Differentiation of constant gives zero
lnx+c\ln x + clnx+c
1aln(ax+b)+c\frac{1}{a}\ln(ax+b) + ca1ln(ax+b)+c
Exact area between curve and x-axis over interval
∫u dv=uv−∫v du\int u \, dv = uv - \int v \, du∫udv=uv−∫vdu
Choose uuu in integration by parts
v=dsdtv = \frac{ds}{dt}v=dtds
a=dvdta = \frac{dv}{dt}a=dtdv
W=∫abF(x)dxW = \int_a^b F(x)dxW=∫abF(x)dx
Separate variables, then integrate both sides
Particular uses initial conditions to find constant
Let v=dydxv = \frac{dy}{dx}v=dxdy, then d2ydx2=vdvdy\frac{d^2y}{dx^2} = v\frac{dv}{dy}dx2d2y=vdydv
P=kQP = kQP=kQ where kkk is constant of proportionality
Choose uuu, find dxdxdx in terms of dududu, substitute, solve, back-sub
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