Integration 2 summary

Key learning points

• Substitution: set $u$ to the inside function and replace $dx$.
• Parts: $\int u\frac{dv}{dx}\,dx=uv-\int v\frac{du}{dx}\,dx$.
• Choose $u$ so that it simplifies when differentiated.
• Finish indefinite integrals with $+C$.

Worked example 1 — Parts

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

Working

Take $u=x$ and $\frac{dv}{dx}=e^x$.

Worked example 2 — Substitution: set to the inside function and replace

Use this method from the Integration 2 sheet: Substitution: set $u$ to the inside function and replace $dx$.

Working

Each key learning point matches a question type on the printable worksheet.

Worked example 3 — Choose so that it simplifies when differentiated

Use this method from the Integration 2 sheet: Choose $u$ so that it simplifies when differentiated.

Working

Each key learning point matches a question type on the printable worksheet.

Worked example 4 — Finish indefinite integrals with

Use this method from the Integration 2 sheet: Finish indefinite integrals with $+C$.

Working

Each key learning point matches a question type on the printable worksheet.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.