Evaluate ∫ x√(x^2 + 4) dx.

Question 28

MediumOriginal question

Evaluate $\int x\sqrt{x^{2} + 4}\,dx$ .

\frac{2}{3}\left(x^{2} + 4\right)^{\frac{3}{2}} + C

Correct answerYour answer

\frac{1}{3}\left(x^{2} + 4\right)^{\frac{3}{2}} + C

Correct answerYour answer

\frac{1}{6}\left(x^{2} + 4\right)^{\frac{3}{2}} + C

Correct answerYour answer

\frac{x^{2}}{3}\left(x^{2} + 4\right)^{\frac{3}{2}} + C

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Put $t = x^{2} + 4$ , so $dt = 2x\,dx$ and $x\,dx = \frac{dt}{2}$ .
$\frac{1}{2}\int t^{1/2}\,dt = \frac{1}{2} \cdot \frac{2}{3}t^{3/2} = \frac{1}{3}(x^{2} + 4)^{3/2} + C$ .

Worth noting

$\frac{2}{3}$ forgets the $\frac{1}{2}$ from $x\,dx = \frac{dt}{2}$ .

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