Question

$\int \frac{\log (x^2+a^2)}{x^2}dx=$

• A. $\frac{-\log (x^2+a^2)}{x}+\frac{2}{a}ta{n}^{-1}\left(\frac{x}{a}\right)+c$
• B. $\frac{\log (x^2+a^2)}{x}+\frac{2}{a}ta{n}^{-1}\left(\frac{x}{a}\right)+c$
• C. $\frac{\log (x^2+a^2)}{x}-\frac{2}{a}ta{n}^{-1}\left(\frac{x}{a}\right)+c$
• D. $-\frac{\log (x^2+a^2)}{x}-\frac{2}{a}ta{n}^{-l}\left(\frac{x}{a}\right)+c$

Answer 1

Answer: (A)

$\frac{-\log (x^2+a^2)}{x}+\frac{2}{a}ta{n}^{-1}\left(\frac{x}{a}\right)+c$

$\int \frac{log(x^2+a^2)}{x^2}dx$

$log(x^2+a^2)\int 1/x^{2}dx-\int (\frac{2x}{x^2+a^2}-[\int \frac{1}{x^2}dx\left]\right)dx$

$=log(x^2+a^2)(-1/x)+2\int \frac{1}{(x^2+a^2)}dx+c$

$=log(x^2+a^2)(-1/x)+\frac{2}{a}ta{n}^{-1}\left(x/a\right)+c$

$=\frac{-log(x^2+a^2)}{x}+\frac{2}{a}ta{n}^{-1}\left(x/a\right)+c$

$\int \frac{log(x^2+a^2)}{x^2}dx=\frac{-log(x^2+a^2)}{x}+\frac{2}{a}ta{n}^{-1}\left(x/a\right)+c$