∫k dx=kx+C\int k\,dx = kx + C∫xn dx=xn+1n+1+C(n≠−1)\int x^n\,dx = \frac{x^{n+1}}{n+1} + C \quad (n \ne -1)∫1x dx=ln∣x∣+C\int \frac{1}{x}\,dx = \ln|x| + C∫11−x2 dx=arcsinx+C\int \frac{1}{\sqrt{1-x^2}}\,dx = \arcsin x + C ∫11+x2 dx=arctanx+C\int \frac{1}{1+x^2}\,dx = \arctan x + C∫ax dx=1lnaax+C(a>0, a≠1)\int a^x\,dx = \frac{1}{\ln a}a^x + C \quad (a > 0,\, a \ne 1)∫cosx dx=sinx+C\int \cos x\,dx = \sin x + C∫sinx dx=−cosx+C\int \sin x\,dx = -\cos x + C∫sec2x dx=tanx+C\int \sec^2 x\,dx = \tan x + C∫csc2x dx=−cotx+C\int \csc^2 x\,dx = -\cot x + C∫secxtanx dx=secx+C\int \sec x \tan x\,dx = \sec x + C∫cscxcotx dx=−cscx+C\int \csc x \cot x\,dx = -\csc x + C∫secx dx=ln∣secx+tanx∣+C\int \sec x\,dx = \ln|\sec x + \tan x| + C∫cscx dx=ln∣cscx−cotx∣+C\int \csc x\,dx = \ln|\csc x - \cot x| + C∫tanx dx=−ln∣cosx∣+C\int \tan x\,dx = -\ln|\cos x| + C∫cotx dx=ln∣sinx∣+C\int \cot x\,dx = \ln|\sin x| + C∫dxx2+a2=1aarctanxa+C(a>0)\int \frac{dx}{x^2 + a^2} = \frac{1}{a}\arctan\frac{x}{a} + C \quad (a > 0)∫dxx2+a2=ln∣x+x2+a2∣+C(a>0)\int \frac{dx}{\sqrt{x^2 + a^2}} = \ln\left|x + \sqrt{x^2 + a^2}\right| + C \quad (a > 0)∫dxa2−x2=arcsinxa+C(a>0)\int \frac{dx}{\sqrt{a^2 - x^2}} = \arcsin\frac{x}{a} + C \quad (a > 0)∫1a2−x2 dx=12aln∣a+xa−x∣+C(a>0)\int \frac{1}{a^2 - x^2}\,dx = \frac{1}{2a}\ln\left|\frac{a+x}{a-x}\right| + C \quad (a > 0)
