Question

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 1

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

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