Def: Fie 𝐹, 𝑓: 𝐼 → ℝ , 𝐼 ⊆ ℝ , 𝐼 interval. 𝐹 este o primitivă pentru 𝑓 dacă:
𝐹′ (𝑥 ) = 𝑓 (𝑥 ), ∀𝑥 ∈ 𝐼.
Primitive uzuale
 ∫ 1 𝑑𝑥 = 𝑥 + 𝒞
 ∫ 𝑥 𝑝 𝑑𝑥 =
𝑥 𝑝+1
𝑝+1
+ 𝒞, 𝑝 ≠ −1
1
 ∫ 𝑑𝑥 = ln|𝑥| + 𝒞
𝑥
𝑎𝑥
 ∫ 𝑎𝑥 𝑑𝑥 =
+ 𝒞, 𝑎 > 0, 𝑎 ≠ 1; ∫ 𝑒 𝑥 𝑑𝑥 = 𝑒 𝑥 + 𝒞
ln 𝑎




∫ sin 𝑥 𝑑𝑥 = − cos 𝑥 + 𝒞
∫ cos 𝑥 𝑑𝑥 = sin 𝑥 + 𝒞
∫ 𝑡𝑔 𝑥 𝑑𝑥 = − ln|cos 𝑥| + 𝒞
∫ 𝑐𝑡𝑔 𝑥 𝑑𝑥 = ln|sin 𝑥| + 𝒞
1
 ∫ 2 𝑑𝑥 = 𝑡𝑔 𝑥 + 𝒞
cos 𝑥
1
 ∫ 2 𝑑𝑥 = −𝑐𝑡𝑔 𝑥 + 𝒞
sin 𝑥
1
𝑥
 ∫ 2 2 𝑑𝑥 = 𝑎𝑟𝑐𝑠𝑖𝑛 + 𝒞
√𝑎 −𝑥
𝑎
1
 ∫ 2
𝑑𝑥 = ln|𝑥 + √𝑥 2 + 𝑎| + 𝒞, 𝑎 ≠ 0
√𝑥 +𝑎
1
1
𝑥
1
1
𝑥−𝑎
 ∫ 2 2 𝑑𝑥 = 𝑎𝑟𝑐𝑡𝑔 + 𝒞, 𝑎 > 0
𝑥 +𝑎
𝑎
𝑎
 ∫ 2 2 𝑑𝑥 = ln | | + 𝒞
𝑥 −𝑎
2𝑎
𝑥+𝑎
Reguli:
 ∫ 𝑎 ⋅ 𝑓 (𝑥 ) 𝑑𝑥 = 𝑎 ⋅ ∫ 𝑓(𝑥 ) 𝑑𝑥
 ∫[𝑓 (𝑥 ) + 𝑔(𝑥)] 𝑑𝑥 = ∫ 𝑓(𝑥 )𝑑𝑥 + ∫ 𝑔(𝑥 )𝑑𝑥