I'm a bit rusty with integration - question below

Question

vocaloid · Answer

$$\int\limits_{ }^{ } \frac{ 4x }{ x^2 + \frac{ 1 }{ x } }$$

vocaloid · Answer

don't want a direct answer, I just want to know where to start

vocaloid · Answer

*should be a dx added into the equation

zepdrix · Answer

It looks like it might be a simple u-substitution hidden in disguise.
Try multiplying top and bottom by x, what happens?

vocaloid · Answer

$$\int\limits_{ }^{ }\frac{ 4x^2 }{ x^3 + 1 }$$

vocaloid · Answer

so I'm guessing I would let u = x^3 + 1

then that gives me du = 3x^2

sweetburger · Answer

yes, perfect

coolor · Answer

*du=3x^2(dx)

zepdrix · Answer

Bottom is a cubic, top is a square,
hmm that works out nicely! :)

coolor · Answer

^`

zepdrix · Answer

$$\large\rm du=3x^2dx$$You could take a couple simple steps and turn the 3 into a 4 so it matches up perfectly with your numerator.

vocaloid · Answer

right, multiply by 4/3

vocaloid · Answer

(4/3)*ln(x^3+1)?

zepdrix · Answer

Yayyy good job \c:/

coolor · Answer

don't forget the constant "c"

vocaloid · Answer

thank you both, I just started differential equations >>

zepdrix · Answer

Ooo fun stuff!