1. \(\int \{f(x) \pm \varphi(x)\} dx = \int f(x) dx \pm \int \varphi(x) dx\)
2. \(\int cf(x) dx = c \int f(x) dx\)

কিছু প্রমিত ফাংশনের যোগজ:

1. \(\int x^n dx = \frac{x^{n+1}}{n+1} + c\) যখন \(n \neq -1\)
2. \(\int \frac{1}{x} dx = \ln|x| + c\)
3. \(\int \frac{f'(x)}{f(x)} dx = \ln|f(x)| + c\)
4. \(\int \sin x \, dx = -\cos x + c\)
5. \(\int \cos x \, dx = \sin x + c\)
6. \(\int \sec^2 x \, dx = \tan x + c\)
7. \(\int \text{cosec}^2 x \, dx = -\cot x + c\)
8. \(\int e^{mx} dx = \frac{1}{m} e^{mx} + c\)
9. \(\int a^x dx = \frac{a^x}{\ln a} + c\)
10. \(\int \text{cosec } x \cot x \, dx = -\text{cosec } x + c\)
11. \(\int \sec x \tan x \, dx = \sec x + c\)
12. \(\int \frac{dx}{\sqrt{1 - x^2}} = \sin^{-1} x + c\)
13. \(\int -\frac{dx}{\sqrt{1 - x^2}} = \cos^{-1} x + c\)
14. \(\int \frac{dx}{1 + x^2} = \tan^{-1} x + c\)
15. \(\int -\frac{dx}{1 + x^2} = \cot^{-1} x + c\)
16. \(\int \frac{dx}{x\sqrt{x^2 - 1}} = \sec^{-1} x + c\)
17. \(\int -\frac{dx}{x\sqrt{x^2 - 1}} = \text{cosec}^{-1} x + c\)
18. \(\int \frac{1}{2\sqrt{x}} dx = \sqrt{x} + c\)