Question

∫[1/(4+x^2)dx = ?

Answer 1

(1/2)ln(4+x^2)+C

Answer 2

trig substitution !

Answer 3

\[4+x^2=4(1+(\frac{x}{2})^2)\]

Answer 4

\[\tan(\theta)=\frac{x}{2} =>\sec^2(\theta) d \theta=\frac{1}{2} dx\]

Answer 5

Messed up... :(

Answer 6

\[\int\limits_{}^{}2 \frac{\sec^2(\theta)}{4(1+\tan^2(\theta))} d \theta\]

Answer 7

\[\frac{1}{2}\int\limits_{}^{}\frac{\sec^2(\theta)}{\sec^2(\theta)} d \theta\]

Answer 8

\[\frac{1}{2}\int\limits_{}^{}1 d \theta\]

Answer 9

\[\frac{1}{2} \cdot \theta+C=\frac{1}{2} \cdot \tan^{-1}(\frac{x}{2})+C\]