Formulario Cálculo Integral
Integrales de funciones algebraicas
1. ∫𝑑𝑥 = 𝑥 + 𝐶
2. ∫𝑘 𝑑𝑥 = 𝑘 ∫𝑑𝑥
3. ∫𝑘 𝑑𝑥 = 𝑘𝑥 +𝐶
4. ∫𝑢 ± 𝑣 𝑑𝑥 = ∫𝑢 𝑑𝑥 ± ∫𝑣 𝑑𝑥
5. ∫𝑥𝑛𝑑𝑥 = 𝑥𝑛+1
𝑛+1 + 𝐶 → 𝑛 ≠ −1
6. ∫𝑥𝑚/𝑛𝑑𝑥 = ( 𝑛
𝑚+𝑛)𝑥𝑚+𝑛
𝑛+𝐶
7. ∫𝑥1/𝑛𝑑𝑥 = ( 𝑛
𝑛+1)𝑥𝑛+1
𝑛+𝐶
8. ∫𝑢𝑛𝑑𝑢 = 𝑢𝑛+1
𝑛+1 + 𝐶 → 𝑛 ≠ −1
9. ∫𝑢1/𝑛𝑑𝑢 = ( 𝑛
𝑛+1)𝑥
10. ∫𝑢𝑚/𝑛 = ( 𝑛
𝑚+𝑛)𝑢𝑚+𝑛
𝑛+𝐶
Integrales de funciones trigonométricas
1. ∫𝑠𝑒𝑛 𝑢 𝑑𝑢 = − cos𝑢+𝐶
2. ∫𝑠𝑒𝑛 𝑘𝑢 𝑑𝑢 = − 1
𝑘𝑐𝑜𝑠 𝑘𝑢 + 𝐶
3. ∫𝑠𝑒𝑛2𝑢 𝑑𝑢 = 𝑢
2−𝑠𝑒𝑛 2𝑢
4+𝐶
4. ∫𝑠𝑒𝑛3𝑢 𝑑𝑢 = − 3
4𝑐𝑜𝑠 𝑢 + 1
12𝑐𝑜𝑠 3𝑢
5. ∫𝑠𝑒𝑛𝑛𝑢 𝑑𝑢 = − 1
𝑛𝑐𝑜𝑠 𝑢 𝑠𝑒𝑛𝑛−1𝑢+ 𝑛−1
𝑛∫𝑠𝑒𝑛𝑛−2𝑢 𝑑𝑢
6. ∫cos𝑢 𝑑𝑢 = 𝑠𝑒𝑛 𝑢 + 𝐶
7. ∫𝑐𝑜𝑠 𝑘𝑢 𝑑𝑢 = 1
𝑘𝑠𝑒𝑛 𝑘𝑢+ 𝐶
8. ∫𝑐𝑜𝑠2𝑢 𝑑𝑢 = 𝑢
2+1
4𝑠𝑒𝑛 2𝑢
9. ∫𝑐𝑜𝑠3𝑢 𝑑𝑢 = 3
4𝑠𝑒𝑛 𝑢 + 1
12𝑠𝑒𝑛 3𝑢 + 𝐶
10. ∫𝑐𝑜𝑠𝑛𝑢 𝑑𝑢 = 1
𝑛𝑠𝑒𝑛 𝑢 𝑐𝑜𝑠𝑛−1𝑢 +𝑛−1
𝑛∫𝑐𝑜𝑠𝑛−2𝑢 𝑑𝑢
11. ∫tan𝑢 𝑑𝑢 = ln(𝑠𝑒𝑐𝑢)+𝐶;−ln(cos𝑢)+ 𝐶
12. ∫𝑡𝑎𝑛2𝑢 𝑑𝑢 = 𝑡𝑎𝑛 𝑢 − 𝑢 + 𝐶
13. ∫𝑡𝑎𝑛𝑛𝑢 𝑑𝑢 = 𝑡𝑎𝑛𝑛−1𝑢
𝑛−1 −∫𝑡𝑎𝑛𝑛−2𝑢 𝑑𝑢
14. ∫𝑐𝑜𝑡 𝑢 𝑑𝑢 = 𝑙𝑛(𝑠𝑒𝑛 𝑢)+𝐶
15. ∫𝑐𝑜𝑡2𝑢 𝑑𝑢 = −𝑐𝑜𝑡 𝑢 − 𝑢 + 𝐶
16. ∫𝑐𝑜𝑡𝑛𝑢 𝑑𝑢 = − 𝑐𝑜𝑡𝑛−1𝑢
𝑛−1 −∫𝑐𝑜𝑡𝑛−2𝑢 𝑑𝑢
17. ∫sec 𝑢 𝑑𝑢 = 𝑙𝑛(𝑠𝑒𝑐 𝑢 + 𝑡𝑎𝑛 𝑢)+𝐶
18. ∫𝑠𝑒𝑐2𝑢 𝑑𝑢 = 𝑡𝑎𝑛 𝑢 + 𝐶
19. ∫𝑐𝑠𝑐 𝑢 𝑑𝑢 = 𝑙𝑛(𝑐𝑠𝑐 𝑢 − 𝑐𝑜𝑡 𝑢)+𝐶
20.
∫𝑐𝑠𝑐2𝑢 𝑑𝑢 = −𝑐𝑜𝑡 𝑢 + 𝐶
21. ∫𝑠𝑒𝑐 𝑢 ∙ 𝑡𝑎𝑛 𝑢 𝑑𝑢 = 𝑠𝑒𝑐 𝑢 + 𝐶
22.
∫𝑐𝑠𝑐 𝑢 ∙ 𝑐𝑜𝑡 𝑢 𝑑𝑢 = −𝑐𝑠𝑐 𝑢 + 𝐶
23.
∫𝑠𝑒𝑛 𝑎𝑢∙ 𝑠𝑒𝑛 𝑏𝑢 𝑑𝑢 = − 𝑠𝑒𝑛(𝑎𝑢+𝑏𝑢)
2(𝑎+𝑏)+𝑠𝑒𝑛(𝑎𝑢−𝑏𝑢)
2(𝑎−𝑏)+𝐶
24.
∫𝑠𝑒𝑛 𝑎𝑢∙ 𝑐𝑜𝑠 𝑏𝑢 𝑑𝑢 = − cos(au+bu)
2(𝑎+𝑏)−cos (au−bu)
2(𝑎−𝑏)+𝐶
25.
∫𝑐𝑜𝑠 𝑎𝑢∙ 𝑐𝑜𝑠 𝑏𝑢 𝑑𝑢 = 𝑠𝑒𝑛(𝑎𝑢+𝑏𝑢)
2(𝑎+𝑏)+𝑠𝑒𝑛(𝑎𝑢−𝑏𝑢)
2(𝑎−𝑏)+𝐶
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