Evaluate: \(\int \dfrac{1}{25 - 9x^2}\,dx\)
Q.11 Evaluate: \(\int \dfrac{1}{25 - 9x^2}\,dx\)
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Answer: \(\dfrac{1}{30}\log\left|\dfrac{5 + 3x}{5 - 3x}\right| + c\)
\(I = \dfrac19\int \dfrac{dx}{\left(\frac53\right)^2 - x^2}\). Using \(\int\dfrac{dx}{a^2 - x^2} = \dfrac{1}{2a}\log\left|\dfrac{a + x}{a - x}\right| + c\) with \(a = \frac53\):
\(I = \dfrac19\cdot\dfrac{1}{2\cdot\frac53}\log\left|\dfrac{\frac53 + x}{\frac53 - x}\right| + c = \dfrac{1}{30}\log\left|\dfrac{5 + 3x}{5 - 3x}\right| + c\).
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· 28 Oct 2026
AI-verified · Oct 2026
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