Question

integral (3x^2 / (squareroot of x^3 +1) )dx =

Answer 1

HI!

Answer 2

this is a u sub for sure

Answer 3

put \(u=x^3+1, du =3x^2dx\) and you get
\[\int \frac{du}{\sqrt{u}}\] right away

Answer 4

you okay after that? write is as
\[\int u^{-\frac{1}{2}}du\] and use the power rule, only the other way
\[\int u^n=\frac{u^{n+1}}{n+1}\]

Answer 5

okay keep going

Answer 6

lol no you keep going
let me know what you get

Answer 7

1/2 ( x^3 +1) ^ -1/2 (3x^2) dx

Answer 8

then 2du = all that minus the 1/2

Answer 9

where does that 1/2 in front come from ?

Answer 10

i guess i did not help much

Answer 11

start here \[\int u^{-\frac{1}{2}}du\]

Answer 12

okay yes i go that far

Answer 13

the derivative of the inside of that bottom square root function is on top
if u=x^3+1
then du/dx=3x^2
so du=3x^2 dx
so ...