Question

Integrate (2x^3)/(1-x^4)^(1/2)dx show work please

Answer 1

Use the substitution x = sqrt(cosy)

Answer 2

try
\[u=1-x^4, du=-4x^3dx,2x^3dx=-\frac{1}{2}du\] and it should pop right out

Answer 3

i wouldn't bother with a trig sub. it may work, but it is easy enough to integrate
\[-\frac{1}{2}\int\frac{du}{\sqrt{u}}\]

Answer 4

the 2x^3dx = -1/2du is a bit strange to me

Answer 5

cancels out very nicely, actually. knowledge of trig subs is a very useful skill to have.

Answer 6

im used to setting my dx = 1/-4x^3

Answer 7

well you are given
\[2x^3\] in the numerator, so you have to cope with it some how

Answer 8

is my approach incorrect?

Answer 9

would it be wrong to use dx = 1/-4x^3

Answer 10

yes that will not work

Answer 11

strange to me, i was under the assumption that all i had to do with my du was set it in terms of dx

Answer 12

this is a set up for a u - sub because you have a composite function in
\[\frac{1}{\sqrt{1-x^4}}\] and the derivative of the inside piece, that is the derivative of
\[1-x^4\] is pretty much staring you in the face in the numerator. you are only off by a constant

Answer 13

\[u(x)=1-x^4, \frac{du}{dx}=-4x^3, du = -4x^3dx \] etc

Answer 14

up to there i understand, how did you go from that DU to the DX that you set up?

Answer 15

?