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Tabla de integrales indefinidas
- 1. 1.-∫ 𝑑𝑥 = 𝑥 + 𝐶 2.-∫ 𝑎𝑑𝑥 = 𝑎𝑥 + 𝐶 3.-∫ 𝑎𝑑𝑤 = 𝑎 ∫ 𝑑𝑤 4.-∫ 𝑥 𝑛 𝑑𝑥 = 𝑥 𝑛+1 𝑛+1 + 𝐶 5.- ∫( 𝑑𝑢 + 𝑑𝑣 − 𝑑𝑤) = ∫ 𝑑𝑢 + ∫ 𝑑𝑣 − ∫ 𝑑𝑤 6.-∫ 𝑤 𝑛 𝑑𝑤 = 𝑤 𝑛+1 𝑛+1 + 𝐶, n ≠ -1 7.-∫ 𝑑𝑤 𝑤 = ln| 𝑤| + 𝑐 8.-∫ 𝑎 𝑤 𝑑𝑤 = 𝑎 𝑤 𝑙𝑛𝑎 + 𝐶 9.-∫ 𝑒 𝑤 𝑑𝑤 = 𝑒 𝑤 + 𝐶 10.-∫ 𝑠𝑒𝑛𝑤 𝑑𝑤 = −cos 𝑤 + 𝐶 11.-∫ 𝑐𝑜𝑠𝑤 𝑑𝑤 = 𝑠𝑒𝑛𝑤 + 𝐶 12.-∫ 𝑠𝑒𝑐2 𝑤𝑑𝑤 = 𝑡𝑔𝑤 + 𝐶 13.-∫ 𝑐𝑠𝑐2 𝑤𝑑𝑤 = −𝑐𝑡𝑔𝑤 + 𝐶 14.-∫ 𝑠𝑒𝑐𝑤 𝑡𝑔 𝑤 𝑑𝑤 = 𝑠𝑒𝑐𝑤 + 𝐶 15.-∫ 𝑡𝑔𝑤 𝑑𝑤 = −𝑙𝑛 𝑐𝑜𝑠 𝑤 + 𝐶 = 𝑙𝑛𝑠𝑒𝑐𝑤 + 𝐶 16.-∫ 𝑐𝑡𝑔𝑤 𝑑𝑤 = 𝑙𝑛𝑠𝑒𝑛 𝑤 + 𝐶 17.-∫ 𝑐𝑠𝑐𝑤 𝑐𝑡𝑔 𝑤 𝑑𝑤 = −𝑐𝑠𝑐𝑤 + 𝐶 18.-∫ 𝑑𝑤 𝑤2+𝑎2 = 1 𝑎 𝑎𝑟𝑐𝑡𝑔 𝑤 𝑎 + 𝐶 19.-∫ 𝑑𝑤 𝑤2−𝑎2 = 1 2𝑎 𝑙𝑛 𝑤−𝑎 𝑤+𝑎 + 𝐶 20.-∫ 𝑑𝑤 𝑎2−𝑤2 = 1 2𝑎 𝑙𝑛 𝑎+𝑤 𝑎−𝑤 + 𝐶
- 2. 21.-∫ 𝑑𝑤 √𝑎2−𝑤2 = 𝑎𝑟𝑐 𝑠𝑒𝑛 𝑤 𝑎 + 𝐶 22.-∫ sec 𝑤 𝑑𝑤 =∫ 𝑑𝑤 𝑐𝑜𝑠𝑤 = 𝑙𝑛(sec 𝑤 + 𝑡𝑔 𝑤) + 𝐶 = 𝑙𝑛 𝑡𝑔( 𝑤 2 + 𝜋 4 ) + 𝐶 23.-∫ csc 𝑤 𝑑𝑤 =∫ 𝑑𝑤 𝑠𝑒𝑛𝑤 = 𝑙𝑛( 𝑐𝑠𝑐𝑤 − 𝑐𝑡𝑔 𝑤) + 𝐶 = 𝑙𝑛𝑡𝑔 𝑊 2 + 𝐶 24.-∫ 𝑠𝑒𝑛2 𝑤 𝑑𝑤 = 1 2 𝑤 − 1 4 𝑠𝑒𝑛2𝑤 + 𝐶 25.-∫ 𝑐𝑜𝑠2 𝑤 𝑑𝑤 = 1 2 𝑤 + 1 4 𝑠𝑒𝑛2𝑤 + 𝐶 26.-∫ 𝑐𝑜𝑠 𝑛 𝑤 𝑠𝑒𝑛 𝑤 𝑑𝑤 = − 𝑐𝑜𝑠 𝑛+1 𝑤 𝑛+1 + 𝐶 27.-∫ 𝑠𝑒𝑛 𝑛 𝑤 𝑐𝑜𝑠 𝑤 𝑑𝑤 = 𝑠𝑒𝑛 𝑛+1 𝑤 𝑛+1 + 𝐶 28.-∫ 𝑠𝑒𝑛 𝑚𝑤 𝑠𝑒𝑛 𝑛𝑤 𝑑𝑤 = − 𝑠𝑒𝑛( 𝑚+𝑛) 𝑤 2(𝑚+𝑛) + 𝑠𝑒𝑛( 𝑚−𝑛) 𝑤 2(𝑚−𝑛) + 𝐶 29.-∫ 𝑐𝑜𝑠 𝑚𝑤 𝑐𝑜𝑠 𝑛𝑤 𝑑𝑤 = 𝑠𝑒𝑛( 𝑚+𝑛) 𝑤 2(𝑚+𝑛) + 𝑠𝑒𝑛( 𝑚−𝑛) 𝑤 2(𝑚−𝑛) + 𝐶 30.-∫ 𝑠𝑒𝑛 𝑚𝑤 𝑐𝑜𝑠 𝑛𝑤 𝑑𝑤 = − 𝑐𝑜𝑠( 𝑚+𝑛) 𝑤 2(𝑚+𝑛) − 𝑐𝑜𝑠( 𝑚−𝑛) 𝑤 2(𝑚−𝑛) + 𝐶 31.-∫ 𝑑𝑤 𝑤2−𝑎2 = 1 2𝑎 𝑙𝑛 𝑤−𝑎 𝑤+𝑎 + 𝐶 32.- ∫ 𝑑𝑤 𝑎2−𝑤2 = 1 2𝑎 𝑙𝑛 𝑎+𝑤 𝑎−𝑤 + 𝐶 33.-∫ 𝑑𝑤 √ 𝑤2±𝑎2 = ln(𝑤 + √𝑤 2 ± 𝑎2) + 𝐶 34.-∫ √ 𝑎2 − 𝑤2 𝑑𝑤 = 𝑤 2 √ 𝑎2 − 𝑤2 + 𝑎2 2 𝑎𝑟𝑐 𝑠𝑒𝑛 𝑤 𝑎 + 𝐶 35.-∫ √𝑤2 ± 𝑎2 𝑑𝑤 = 𝑤 2 √𝑤2 ± 𝑎2 ± 𝑎2 2 ln(𝑤 + √ 𝑤2 ± 𝑎2)) + 𝐶