Power Rule
\(\int x^2 dx = \frac{x^3}{3} + C\)
積分計算機
ステップバイステップの解法で定積分と不定積分を計算
結果
値を入力して計算をクリックして結果を表示してください。
Theory & Formula
Integration is the reverse process of differentiation. It finds the antiderivative of a function, representing the area under a curve.
Common integration rules:
- Power Rule: \(\int x^n dx = \frac{x^{n+1}}{n+1} + C \quad (n \neq -1)\)
- Constant Rule: \(\int c dx = cx + C\)
- Sum Rule: \(\int [f + g] dx = \int f dx + \int g dx\)
- Trigonometric: \(\int \sin(x) dx = -\cos(x) + C\), \(\int \cos(x) dx = \sin(x) + C\)
- Exponential: \(\int e^x dx = e^x + C\)
- Definite Integral: \(\int_{a}^{b} f(x) dx = F(b) - F(a)\)
Worked Examples
Trigonometric
\(\int \sin(x) dx = -\cos(x) + C\)
Exponential
\(\int e^x dx = e^x + C\)