Methods Of Integration

Concept: Use substitution:
Step 1: Differentiate.
Step 2: Expression becomes:
Step 3: Scaling gives:

Concept: Use reverse product rule: Step 1: Differentiate RHS. Step 2: Step 3:

Concept: Use identity: and simplify rational trigonometric expressions.
Step 1: Rewrite the integrand.
Step 2: Use symmetry. Let Also,
Step 3: Add both: But since limits symmetry gives half again,

Concept: To solve:
Step 1: Integrate both sides.
Step 2:
Step 3: Rearranging,