این بخش شامل فرمولهای ساده و اثباتی انتگرال هستند:

\int af(x)\,dx = a\int f(x)\,dx \qquad\mbox{(}a \neq 0 \mbox{, constant)}\,\!
\int [f(x) + g(x)]\,dx = \int f(x)\,dx + \int g(x)\,dx
\int f'(x)g(x)\,dx = f(x)g(x) - \int f(x)g'(x)\,dx
\int {f'(x)\over f(x)}\,dx= \ln{\left|f(x)\right|} + C
\int {f'(x) f(x)}\,dx= {1 \over 2} [ f(x) ]^2 + C
\int [f(x)]^n f'(x)\,dx = {[f(x)]^{n+1} \over n+1} + C \qquad\mbox{(for } n\neq -1\mbox{)}\,\!

فرمولهای این بخش کاربردی هستند و میتوان از آنها در حل مسائل عددی استفاده کرد:

\int \,{\rm d}x = x + C
\int x^n\,{\rm d}x = \frac{x^{n+1}}{n+1} + C\qquad\mbox{ if }n \ne -1
\int {dx \over x} = \ln{\left|x\right|} + C
\int {dx \over {a^2+x^2}} = {1 \over a}\arctan {x \over a} + C

فرمولهای این بخش برای حل انتگرالهای مثلثاتی هستند:

\int {dx \over \sqrt{a^2-x^2}} = \sin^{-1} {x \over a} + C
\int {-dx \over \sqrt{a^2-x^2}} = \cos^{-1} {x \over a} + C
\int {dx \over x \sqrt{x^2-a^2}} = {1 \over a} \sec^{-1} {|x| \over a} + C
\int \sin{x}\, dx = -\cos{x} + C
\int \cos{x}\, dx = \sin{x} + C
\int \tan{x} \, dx = -\ln{\left| \cos {x} \right|} + C
\int \cot{x} \, dx = \ln{\left| \sin{x} \right|} + C
\int \sec{x} \, dx = \ln{\left| \sec{x} + \tan{x}\right|} + C
\int \csc{x} \, dx = \ln{\left| \csc{x} - \cot{x}\right|} + C
\int \sec^2 x \, dx = \tan x + C
\int \csc^2 x \, dx = -\cot x + C
\int \sec{x} \, \tan{x} \, dx = \sec{x} + C
\int \csc{x} \, \cot{x} \, dx = - \csc{x} + C
\int \sin^2 x \, dx = \frac{1}{2}(x - \sin x \cos x) + C
 
\int \cos^2 x \, dx = \frac{1}{2}(x + \sin x \cos x) + C
 
\int \sec^3 x \, dx = \frac{1}{2}\sec x \tan x + \frac{1}{2}\ln|\sec x + \tan x| + C
\int \sin^n x \, dx = - \frac{\sin^{n-1} {x} \cos {x}}{n} + \frac{n-1}{n} \int \sin^{n-2}{x} \, dx
 
\int \cos^n x \, dx = \frac{\cos^{n-1} {x} \sin {x}}{n} + \frac{n-1}{n} \int \cos^{n-2}{x} \, dx
 
\int \arctan{x} \, dx = x \, \arctan{x} - \frac{1}{2} \ln{\left| 1 + x^2\right|} + C
\int \sinh x \, dx = \cosh x + C
\int \cosh x \, dx = \sinh x + C
\int \tanh x \, dx = \ln| \cosh x | + C
\int \mbox{csch}\,x \, dx = \ln\left| \tanh {x \over2}\right| + C
\int \mbox{sech}\,x \, dx = \arctan(\sinh x) + C
\int \coth x \, dx = \ln| \sinh x | + C
\int \mbox{sech}^2 x\, dx = \tanh x + C