Question:
\[
\int \frac{dx}{25-x^2}=
\]
\[
\int \frac{dx}{25-x^2}=
\]
Show Hint
For \(\int\frac{dx}{a^2-x^2}\), use \(\frac{1}{2a}\log\left|\frac{a+x}{a-x}\right|+c\).
Updated On: May 7, 2026
- \(\frac{1}{5}\log\left|\frac{x-5}{x+5}\right|+c\)
- \(\frac{1}{5}\log\left|\frac{x+5}{x-5}\right|+c\)
- \(\frac{1}{10}\log\left|\frac{5+x}{5-x}\right|+c\)
- \(\frac{1}{10}\log\left|\frac{5-x}{5+x}\right|+c\)
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The Correct Option is C
Solution and Explanation
Step 1: Use standard formula: \[ \int\frac{dx}{a^2-x^2} = \frac{1}{2a}\log\left|\frac{a+x}{a-x}\right|+c \]
Step 2: Here: \[ a^2=25 \] \[ a=5 \]
Step 3: \[ \int\frac{dx}{25-x^2} = \frac{1}{2(5)} \log\left|\frac{5+x}{5-x}\right|+c \] \[ =\frac{1}{10}\log\left|\frac{5+x}{5-x}\right|+c \] \[ \boxed{\frac{1}{10}\log\left|\frac{5+x}{5-x}\right|+c} \]
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