Question

I'm a bit rusty with integration - question below

Answer 1

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

Answer 2

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

Answer 3

*should be a dx added into the equation

Answer 4

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

Answer 5

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

Answer 6

so I'm guessing I would let u = x^3 + 1

then that gives me du = 3x^2

Answer 7

yes, perfect

Answer 8

*du=3x^2(dx)

Answer 9

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

Answer 10

^`

Answer 11

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

Answer 12

right, multiply by 4/3

Answer 13

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

Answer 14

Yayyy good job \c:/

Answer 15

don't forget the constant "c"

Answer 16

thank you both, I just started differential equations >>

Answer 17

Ooo fun stuff!