Integrate \frac{dx}{\sqrt{x^2+36}}.

Category: QuestionsIntegrate \frac{dx}{\sqrt{x^2+36}}.
Editor">Editor Staff asked 11 months ago

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
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
Editor">Editor Staff answered 11 months ago

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