हिन्दी में पढ़ेंHome › Formulas › Calculus › Standard integrals
Standard integrals formulas
16 formulas for Standard integrals, from the Calculus section of the Quantix formula library. Tap 🧮 next to a formula to solve it for any variable with step-by-step working.
| Name | Formula | Note |
|---|---|---|
| Power | ∫ xⁿ dx = xⁿ⁺¹/(n + 1) + C, n ≠ −1 | |
| 1/x | ∫ dx/x = ln|x| + C | |
| Exponential | ∫ eˣ dx = eˣ + C; ∫ aˣ dx = aˣ/ln a + C | |
| sin, cos | ∫ sin x dx = −cos x + C; ∫ cos x dx = sin x + C | |
| sec², cosec² | ∫ sec²x dx = tan x + C; ∫ cosec²x dx = −cot x + C | |
| tan, cot | ∫ tan x dx = ln|sec x| + C; ∫ cot x dx = ln|sin x| + C | |
| sec | ∫ sec x dx = ln|sec x + tan x| + C | |
| cosec | ∫ cosec x dx = ln|cosec x − cot x| + C | |
| 1/(a² + x²) | (1/a) tan⁻¹(x/a) + C | |
| 1/√(a² − x²) | sin⁻¹(x/a) + C | |
| 1/(x² − a²) | (1/2a) ln|(x − a)/(x + a)| + C | |
| 1/(a² − x²) | (1/2a) ln|(a + x)/(a − x)| + C | |
| 1/√(x² ± a²) | ln|x + √(x² ± a²)| + C | |
| √(a² − x²) | (x/2)√(a² − x²) + (a²/2) sin⁻¹(x/a) + C | |
| √(x² + a²) | (x/2)√(x² + a²) + (a²/2) ln|x + √(x² + a²)| + C | |
| eˣ[f(x) + f′(x)] | eˣ f(x) + C |
Open in the interactive Formula Library