FÓRMULAS FUNDAMENTALES DE INTEGRACIÓN
1.∫𝑑(𝑥)= 𝑥 + 𝑐
2. ∫(𝑢 + 𝑣)𝑑𝑥 =∫𝑢 𝑑𝑥 +∫𝑣 𝑑𝑥
3. ∫𝑘 𝑢 𝑑𝑢 = 𝑘 ∫𝑢𝑑𝑢 ,
siendo k una constante
4. ∫𝑢𝑛𝑑𝑢 =𝑢𝑛+1
𝑛+1 + 𝑐 , 𝑛 ≠ −1
5. ∫𝑑𝑢
𝑢=ln|𝑢|+ 𝑐
6. ∫𝑎𝑢𝑑𝑢 =𝑎𝑢
ln𝑎+ 𝑐, 𝑎 > 0, 𝑎 ≠ 1
7. ∫𝑒𝑢𝑑𝑢 =𝑒𝑢+ 𝑐
8. ∫𝑠𝑒𝑛 𝑢 𝑑𝑢 = −cos 𝑢 + 𝑐
9. ∫cos 𝑢 𝑑𝑢 = 𝑠𝑒𝑛 𝑢 + 𝑐
10. ∫tan𝑢 𝑑𝑢 =ln|sec 𝑢 |+ 𝑐
11. ∫cot 𝑢 𝑑𝑢 = ln|𝑠𝑒𝑛 𝑢 |+ 𝑐
12. ∫sec 𝑢 𝑑𝑢 =ln|sec 𝑢 + tan𝑢|+ 𝑐
13. ∫csc 𝑢 𝑑𝑢 =ln|csc 𝑢 − cot 𝑢 |+ 𝑐
14. ∫𝑠𝑒𝑐2𝑢 𝑑𝑢 =tan𝑢 + 𝑐
15. ∫𝑐𝑠𝑐2𝑢 𝑑𝑢 = − cot 𝑢 + 𝑐
16. ∫sec𝑢 tan𝑢 𝑑𝑢 = sec 𝑢 + 𝑐
17. ∫csc 𝑢cot 𝑢 𝑑𝑢 = − csc 𝑢 + 𝑐
18. 𝑑𝑢
√𝑎2−𝑢2= 𝑎𝑟𝑐 𝑠𝑒𝑛 𝑢
𝑎+ 𝑐
19. ∫𝑑𝑢
𝑎2+𝑢2=1
𝑎𝑎𝑟𝑐tan𝑢
𝑎+ 𝑐
20. ∫𝑑𝑢
𝑢√𝑢2−𝑎2=1
𝑎𝑎𝑟𝑐sec𝑢
𝑎+ 𝑐
21. ∫𝑑𝑢
𝑢2−𝑎2= 1
2𝑎 ln|𝑢−𝑎
𝑢+𝑎|+ 𝑐
22. ∫𝑑𝑢
𝑎2−𝑢2= 1
2𝑎 ln|𝑎+𝑢
𝑎−𝑢|+ 𝑐
23. ∫𝑑𝑢
√𝑢2+𝑎2=ln(𝑢 + √𝑢2+ 𝑎2)+ 𝑐
24. ∫𝑑𝑢
√𝑢2−𝑎2=ln(𝑢 + √𝑢2− 𝑎2)+ 𝑐
25. ∫√𝑎2− 𝑢2𝑑𝑢 = 1
2𝑢√𝑎2− 𝑢2+1
2𝑎2𝑎𝑟𝑐 𝑠𝑒𝑛 𝑢
𝑎+ 𝑐
26. ∫√𝑢2+ 𝑎2𝑑𝑢 = 1
2𝑢√𝑢2+ 𝑎2+1
2𝑎2 ln(𝑢 + √𝑢2+ 𝑎2)+ 𝑐
27.∫√𝑢2− 𝑎2𝑑𝑢 = 1
2𝑢√𝑢2− 𝑎2−1
2𝑎2 ln|𝑢 + √𝑢2− 𝑎2|+ 𝑐
Identidades Trigonométricas
Relaciones Recíprocas
𝑠𝑒𝑛𝑥 = 1
𝑐𝑠𝑐𝑥 𝑐𝑜𝑠𝑥 = 1
𝑠𝑒𝑐𝑥 𝑡𝑎𝑛𝑥 = 1
𝑐𝑜𝑡𝑥
𝑐𝑜𝑡𝑥 = 1
𝑡𝑎𝑛𝑥 𝑠𝑒𝑐 = 1
𝑐𝑜𝑠𝑥 𝑐𝑠𝑐𝑥 = 1
𝑠𝑒𝑛𝑥
Relaciones Cocientes
𝑡𝑎𝑛𝑥 = 𝑠𝑒𝑛𝑥
𝑐𝑜𝑠𝑥 𝐶𝑜𝑡𝑥 = 𝑐𝑜𝑠𝑥
𝑠𝑒𝑛𝑥
Relaciones Pitagóricas
𝑠𝑒𝑛2𝑥 + 𝑐𝑜𝑠2𝑥 = 1 1 + 𝑡𝑎𝑛2𝑥 = 𝑠𝑒𝑐2𝑥
1 + 𝑐𝑜𝑡2𝑥 = 𝑐𝑠𝑐2𝑥
