Evaluate ∫ 1/(√(x^2 + 9)) dx.

Indefinite Integrals · Question 49 of 90

Question 49

MediumOriginal question

Evaluate $\int \frac{1}{\sqrt{x^{2} + 9}}\,dx$ .

\log\left|x + \sqrt{x^2 + 9}\right| + C

Correct answerYour answer

\sin^{-1}\frac{x}{3} + C

Correct answerYour answer

\frac{1}{3}\tan^{-1}\frac{x}{3} + C

Correct answerYour answer

2\sqrt{x^2 + 9} + C

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$\int \frac{dx}{\sqrt{x^2 + a^2}} = \log\left|x + \sqrt{x^2 + a^2}\right| + C$ .
With $a = 3$ : $\log\left|x + \sqrt{x^2 + 9}\right| + C$ .

Worth noting

$\sin^{-1}\frac{x}{3}$ is for $\sqrt{9 - x^2}$ , with the minus sign inside.

Ten questions from Indefinite Integrals, at your own pace.

Ten questions from Indefinite Integrals, at your own pace.