Compute ∫ 2x sin(x²) dx using substitution:
A$\sin(x^2) + C$
B$\cos(x^2) + C$
C$-\cos(x^2) + C$
D$x^2 \cos(x^2) + C$
Answer & Solution
Correct answer: C. $-\cos(x^2) + C$
Let u = x², du = 2x dx → ∫sin(u) du = -cos(u) + C = -cos(x²) + C. Substitution exploits the chain rule in reverse.
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