8.2.5

Integration by Parts - Practice

Test yourself

What is Integration by Parts?

Integration by parts is a method used to integrate the product of two functions. It uses the product rule of differentiation to form an equation that lets us rewrite the integral in a simpler way.

Illustrative background for Integration by partsIllustrative background for Integration by parts ?? "content

Integration by parts

  • The equation for integration by parts is:
    • udvdxdx=uvvdudxdx\int u\frac{dv}{dx}dx = uv-\int v\frac{du}{dx}dx
  • This equation is included in the formula booklet, although it is not named, so you'll need to remember which one it is!
Illustrative background for Choosing functionsIllustrative background for Choosing functions ?? "content

Choosing functions

  • In order to use the integration by parts equation, we need to choose which function is uu and which function is dvdx\frac{dv}{dx}.
  • The combination you choose should make the integral vdudxdx\int v \frac{du}{dx}dx simpler than the original integral you need to solve.
Illustrative background for Constant of integrationIllustrative background for Constant of integration ?? "content

Constant of integration

  • The constant of integration is only included at the very end of the calculation.

Jump to other topics

1Proof

2Algebra & Functions

2.1Powers & Roots

2.2Quadratic Equations

2.3Inequalities

2.4Polynomials

2.5Graphs

2.6Functions

2.7Transformation of Graphs

2.8Partial Fractions (A2 Only)

3Coordinate Geometry

4Sequences & Series

5Trigonometry

6Exponentials & Logarithms

7Differentiation

8Integration

9Numerical Methods

10Vectors

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