MCQ
$\int_1^3\left(\frac{x^2+1}{4 x}\right)^{-1} d x=$
- A$\log 5$
- B$\frac{1}{2} \log 5$
- ✓$\log 25$
- D$\log 100$
✓
Answer
Correct option: C.
$\log 25$
(C)
$\int_1^3\left(\frac{x^2+1}{4 x}\right)^{-1} d x$
$\begin{array}{l}=2 \int_1^3 \frac{2 x}{1+x^2} d x \\ =2\left[\log \left(1+x^2\right)\right]_1^3 \\ =2(\log 10-\log 2) \\ =\log \left(\frac{10}{2}\right)^2 \\ =\log 25\end{array}$
$\int_1^3\left(\frac{x^2+1}{4 x}\right)^{-1} d x$
$\begin{array}{l}=2 \int_1^3 \frac{2 x}{1+x^2} d x \\ =2\left[\log \left(1+x^2\right)\right]_1^3 \\ =2(\log 10-\log 2) \\ =\log \left(\frac{10}{2}\right)^2 \\ =\log 25\end{array}$
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