Question

How to integrate the function?

Answer 1

partial fracs

Answer 2

yeah ^

Answer 3

\[\int\frac{1}{x} - \frac{x}{x^2+1}dx\]

Answer 4

the first integral is a logarithmic, the second is a simple u-sub

Answer 5

http://tutorial.math.lamar.edu/Classes/CalcII/PartialFractions.aspx

Answer 6

Alternative: \[\Large x= \tan \theta \\ \Large dx = \sec^2 \theta d \theta \]\[\Large \int\limits \frac{\sec^2 \theta d \theta}{\tan \theta(\tan^2 \theta + 1)} = \Large \int\limits \frac{\sec^2 \theta d \theta}{\tan \theta \sec^2 \theta} = \int\limits \frac{\cos \theta}{ \sin \theta} d \theta\] Which is \[\Large \ln|\sin \theta| +C= \ln | \frac{x}{ \sqrt{x^2+1}}|+C\]