Find \int \frac{3dx}{9+x^2}.

Category: QuestionsFind \int \frac{3dx}{9+x^2}.
Editor">Editor Staff asked 11 months ago

Find \int \frac{3dx}{9+x^2}.
(a) tan^{-1}⁡\frac{x}{2}+C
(b) tan^{-1}⁡\frac{x}{3}+C
(c) tan^{-1}\frac{x}{5}+C
(d) tan^{-1}⁡\frac{x}{4}+C
The question was asked in an internship interview.
My question is from Integrals of Some Particular Functions topic in portion 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

Correct option is (b) tan^{-1}⁡\frac{x}{3}+C
The best I can explain: \int \frac{3dx}{9+x^2}=3\int \frac{dx}{3^2+x^2}
Using the formula \int \frac{dx}{a^2+x^2}=\frac{1}{a} tan^{-1}\frac{⁡x}{a}+C
∴3\int \frac{dx}{x^2+3^2}=3\left (\frac{1}{3} tan^{-1}⁡\frac{x}{3}\right )+3C_1
3\int \frac{dx}{x^2+3^2}=tan^{-1}⁡\frac{x}{3}+C.