Techniques of Integration · Substitution Methods
u-Substitution
The reverse of the chain rule. Identify an inner function u = g(x), compute du = g'(x) dx, and substitute.
- 0 variables
- 3 worked examples
- 16 in Techniques of Integration
Worked examples
Find ∫ 2x cos(x²) dx.
- Let u = x², du = 2x dx
- ∫ cos(u) du = sin(u) + C
- Back-substitute: sin(x²) + C
Answer: sin(x²) + C
2 more worked examplesPremium
Find ∫ eˢⁱⁿˣ cos x dx.
Step-by-step solution locked.
Find ∫ x/(x²+1) dx.
Step-by-step solution locked.
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Practice
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