Formulario Cálculo Integral
∫𝑑𝑥 = 𝑥 + 𝐶
∫(𝑢 ± 𝑣) 𝑑𝑥 = ∫ 𝑢 𝑑𝑥 ± ∫ 𝑣 𝑑𝑥
∫ 𝑘 𝑢 𝑑𝑢 = 𝑘 ∫ 𝑢 𝑑𝑢
∫𝑥𝑛𝑑𝑥 = 𝑥𝑛+1
𝑛+ 1+ 𝐶 𝑑𝑜𝑛𝑑𝑒 𝑛 ≠ −1
∫𝑢𝑛 𝑑𝑢 = 𝑢𝑛+1
𝑛+ 1+ 𝐶 𝑑𝑜𝑛𝑑𝑒 𝑛 ≠ −1
∫𝑑𝑥
𝑥=ln|𝑥|+𝐶
∫𝑑𝑢
𝑢=ln|𝑢|+𝐶
∫1
(𝑥±𝑘)𝑑𝑥 = ln|𝑥±𝑘|+𝐶
∫𝑎𝑢𝑑𝑢 = 𝑎𝑢
ln𝑎+ 𝐶,𝑎 > 0,𝑎 ≠1
∫𝑥𝑒𝑘𝑥𝑑𝑥 = 𝑒𝑘𝑥
𝑘(𝑥−1
𝑘)+𝐶
∫ 𝑠𝑒𝑛 𝑢 𝑑𝑢 = − cos𝑢+𝐶
∫ 𝑠𝑒𝑛 𝑘𝑢 𝑑𝑢 = − 1
𝑘𝑐𝑜𝑠 𝑘𝑢+𝐶
∫cos𝑢 𝑑𝑢 = 𝑠𝑒𝑛 𝑢 + 𝐶
∫cos𝑘𝑢 𝑑𝑢 = 1
𝑘𝑠𝑒𝑛 𝑘𝑢+𝐶
∫tan𝑢 𝑑𝑢 = ln |sec𝑢 | + 𝐶
∫cot𝑢 𝑑𝑢 = ln |𝑠𝑒𝑛 𝑢 | + 𝐶
∫ sec𝑢 𝑑𝑢 = ln |sec𝑢 + tan𝑢 | + 𝐶
∫ csc𝑢 𝑑𝑢 = 𝑙𝑛|csc𝑢−cot𝑢|+𝐶
∫𝑠𝑒𝑛2𝑢 𝑑𝑢 = 1
2(𝑢 − 𝑠𝑒𝑛 𝑢 ∙ cos𝑢) +𝐶
∫𝑐𝑜𝑠2𝑢 𝑑𝑢 = 1
2(𝑢 + 𝑠𝑒𝑛 𝑢 ∙ cos𝑢) +𝐶
∫𝑡𝑎𝑛2𝑢 𝑑𝑢 = tan𝑢−𝑢 + 𝐶
∫𝑐𝑜𝑡2𝑢 𝑑𝑢 = − 𝑢 − cot𝑢+ 𝐶
∫𝑠𝑒𝑐2𝑢 𝑑𝑢 = tan𝑢 + 𝐶
∫𝑐𝑠𝑐2𝑢 𝑑𝑢 = − cot𝑢+𝐶
∫𝑑𝑢
√𝑎2+𝑢2= 𝑎𝑟𝑐𝑠𝑒𝑛 𝑢
𝑎+𝐶
∫𝑑𝑢
𝑎2+𝑢2=1
𝑎arctan𝑢
𝑎+𝐶
∫𝑑𝑢
𝑢√𝑢2−𝑎2=1
𝑎arcsec𝑢
𝑎+𝐶
∫𝑑𝑢
𝑢2−𝑎2=1
2𝑎ln|𝑢 −𝑎
𝑢+ 𝑎| +𝐶
∫𝑑𝑢
𝑎2−𝑢2=1
2𝑎ln|𝑎 +𝑢
𝑎−𝑢| + 𝐶
∫𝑑𝑢
√𝑢2+𝑎2=ln|𝑢 +√𝑢2+𝑎2|+𝐶
∫𝑑𝑢
√𝑢2−𝑎2=ln|𝑢 +√𝑢2−𝑎2| + 𝐶
