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After u = x² + 1, the integral of x times the square root of x² + 1 becomes which function?
A(x² + 1)^(3/2) + C
B(x² + 1)^(3/2)/2 + C
C(x² + 1)^(3/2)/3 + C
D(2/3)(x² + 1)^(3/2) + C
Answer & Solution
Correct answer: C. (x² + 1)^(3/2)/3 + C
Putting u = x² + 1 gives x dx = du/2, so the integral is (1/2)(2/3)u^(3/2) = u^(3/2)/3.
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