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Mathematics/U-Substitution
Teaching

Problem

∫ 2x(x² + 1)³ dx

1

Let u = x² + 1

Choose the inner function

2

du = 2x dx

Differentiate both sides

3

∫ u³ du

Substitute — much simpler!

4

= u&sup4;/4 + C = (x²+1)&sup4;/4 + C

Substitute back

Chat
TutorWe substitute u = x²+1 because its derivative 2x already appears in the integrand. This is the key pattern to recognize.
Why did we pick u = x²+1 and not something else?
TutorLook at the integrand: 2x is the derivative of x²+1. When you see a function and its derivative together, that's your signal for u-sub.
Now try this one: ∫ 3x² cos(x³) dx
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