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Integrate \(\frac{dx}{\sqrt{x^2+36}}\).(a) –\(log⁡|x^2+\sqrt{x^2+36}|+C\)(b) \(log⁡|2x+\sqrt{x^2+36}|+C\)(c) –\(log⁡|x^2+\sqrt{x^2+6}|+C\)(d) \(log⁡|x^2+\sqrt{x^2+36}|+C\)I got this question by my school teacher while I was bunking the class.My question is from Integrals of Some Particular Functions topic in section Integrals of Mathematics – Class 12

Answer»

The CORRECT ANSWER is (d) \(log⁡|x^2+\SQRT{x^2+36}|+C\)

Best EXPLANATION: \(\int \frac{dx}{\sqrt{x^2+36}}\)

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

∴\(\int \frac{dx}{\sqrt{x^2+36}}=log⁡|x^2+\sqrt{x^2+36}|+C\)


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