Using the substitution $u = x^2 + 1$, evaluate $\int_{0}^{2} \frac{x}{x^2+1}\, dx$

Question

Accepted Answer

$\frac{1}{2}\ln 5$. With u = x² + 1, du = 2x dx, so x dx = du/2. When x = 0, u = 1; when x = 2, u = 5. The integral becomes (1/2)∫₁⁵ du/u = (1/2)[ln u]₁⁵ = (1/2)(ln5 - ln1) = (1/2)ln5. Option A omits the factor of 1/2.

Answer

A) $\ln 5$

Answer

B) $\frac{1}{2}\ln 5$

Answer

C) $\frac{1}{2}\ln 3$

Answer

D) $2\ln 5$

Using the substitution $u = x^2 + 1$, evaluate $\int_{0}^{2} \frac{x}{x^2+1}\, dx$

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