Integrate the function.
-$$\int \frac { 9 \mathrm { dx } } { \sqrt { 9 + \mathrm { x } ^ { 2 } } }$$
A) $9 \ln \left| x + \sqrt { 9 + x ^ { 2 } } \right| + C$
B) $\frac { 2 } { x ^ { 2 } + 9 } + C$
C) $9 \ln \left| \sqrt { 9 + x ^ { 2 } } \right| + C$
D) $x + \ln \left| 9 + \sqrt { 9 + x ^ { 2 } } \right| + C$

Question

Quizplus · Accepted Answer

This integral can be solved using the trigonometric substitution $x = 3\tan(\theta)$, which simplifies the integral to a form that directly integrates to $9 \ln \left| x + \sqrt { 9 + x ^ { 2 } } \right| + C$.

Integrate the Function ∫9dx9+x2\int \frac { 9 \mathrm { dx } } { \sqrt { 9 + \mathrm { x } ^ { 2 } } }∫9+x2​9dx​

Integrate the Function $\int \frac { 9 \mathrm { dx } } { \sqrt { 9 + \mathrm { x } ^ { 2 } } }$