I=∫_2^3 xx^2+1dx ∫xx^2+1dx=12∫2xx^2+1dx =12log(1+x^2)=F(x) I=F(3) F(2) I=12[log 10 log 5] I=12log 2 ...

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Exponents with Like Bases

∫23 xx2+1dx =

Question

${\int_{2}}^{3} \frac{x}{x^{2} + 1} d x =$

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Solution

$I = {\int_{2}}^{3} \frac{x}{x^{2} + 1} d x$

$\int \frac{x}{x^{2} + 1} d x = \frac{1}{2} \int \frac{2 x}{x^{2} + 1} d x$

$= \frac{1}{2} log (1 + x^{2}) = F (x)$

$I = F (3) - F (2)$
$I = \frac{1}{2} [log 10 - log 5]$

$I = \frac{1}{2} log 2$

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