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Find \(\int \frac{10 \,dx}{\sqrt{x^2-25}}\).(a) –\(log⁡|x+\sqrt{x^2-25}|+C\)(b) \(log⁡|x+\sqrt{x^2-25}|+C\)(c) 10 \( log⁡|x+\sqrt{x^2-25}|+C\)(d) -10 \(log⁡|x+\sqrt{x^2-25}|+C\)I have been asked this question during an interview.My question is from Integrals of Some Particular Functions in section Integrals of Mathematics – Class 12

Answer»

The correct answer is (C) 10 \( log⁡|x+\SQRT{x^2-25}|+C\)

Best explanation: \(\INT \FRAC{10 \,dx}{\sqrt{x^2-25}}=10\int \frac{dx}{\sqrt{x^2-25}}\)

By using the formula \(\int \frac{dx}{\sqrt{x^2-a^2}}=log⁡|x+\sqrt{x^2-a^2}|+C\), we get

∴\(10 \int \frac{dx}{\sqrt{x^2-25}}=10 log⁡|x+\sqrt{x^2-25}|+10C_1\)

=10 \(log⁡|x+\sqrt{x^2-25}|+C\)


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