Question

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 1

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 \(log⁡|x+\sqrt{x^2-25}|+C\)