Integration by Parts

📊 intermediate

$$\int u \, dv = uv - \int v \, du$$

A rule that transforms the integral of a product of functions into other forms.

Variables & Units

$u$

First function (to be differentiated)

Unit: Variable

$dv$

Second function part (to be integrated)

Unit: Differential

Key Information

📐 Derived From

Product Rule for differentiation.

💡 Example

Evaluating $\int x e^x \, dx$.

🔧 Applications

Solving complex differential equations and physics derivations.

⚠️ Constraints

Functions $u$ and $v$ must be differentiable.

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