基本的な導関数と不定積分一覧

  $\displaystyle \frac{d}{dx}x = 1$   $\displaystyle \longrightarrow$   $\displaystyle \int dx = x + C$ (4.7)
  $\displaystyle \frac{d}{dx}x^{n+1}=(n+1)x^n$   $\displaystyle \longrightarrow$   $\displaystyle \int x^n dx=\frac{1}{n+1}x^{n+1}+C, \quad (n\ne-1)$ (4.8)
  $\displaystyle \frac{d}{dx}\log x=\frac{1}{x},\quad(x>0)$   $\displaystyle \longrightarrow$   $\displaystyle \int\frac{1}{x}dx=\log\vert x\vert+C$ (4.9)
  $\displaystyle \frac{d}{dx}e^x=e^x$   $\displaystyle \longrightarrow$   $\displaystyle \int e^xdx=e^x+C$ (4.10)
  $\displaystyle \frac{d}{dx}\sin x=\cos x$   $\displaystyle \longrightarrow$   $\displaystyle \int\cos xdx=\sin x+C$ (4.11)
  $\displaystyle \frac{d}{dx}\cos x=-\sin x$   $\displaystyle \longrightarrow$   $\displaystyle \int \sin xdx=-\cos x+C$ (4.12)
  $\displaystyle \frac{d}{dx}\tan x=\frac{1}{\cos^2 x}=\sec^2 x$   $\displaystyle \longrightarrow$   $\displaystyle \int\frac{1}{\cos^2x}dx = \tan x+C$ (4.13)
  $\displaystyle \frac{d}{dx}\arcsin x=\frac{1}{\sqrt{1-x^2}}$   $\displaystyle \longrightarrow$   $\displaystyle \int\frac{1}{\sqrt{1-x^2}}dx=\arcsin x+C$ (4.14)
  $\displaystyle \frac{d}{dx}\arctan x=\frac{1}{1+x^2}$   $\displaystyle \longrightarrow$   $\displaystyle \int\frac{1}{1+x^2} = \arctan x+C$   (4.15)

物理のかぎプロジェクト / 平成19年1月14日