Simplification of Differential Equation: dy/dx = -2x * e^(x^4)

[Karim]

Hi!
I'm currently stuck on the following question.
I did the following:
dy/dx = -2x * e^(x^4)
y = integral( -2x * e^(x^4))
Used Integration by parts
u' = -2x
v = e^(x^4)
so
integral( -2x * e^(x^4)) =-x^2 * e^(x^4) - integral( -x^2 * 4x^3 * e^(x^4))
I'm confused as to how I can simplify this to the options below. Did I go about it the wrong away?

 

[skeeter]

Instead of trying to work out the integral, I would take the derivative of each choice ...

 

[Karim]

Derivative only of the integral or of the constants as well?

 

[blamocur]

Derivative only of the integral or of the constants as well?

Surely you know how to differentiate a constant

 

[Karim]

Surely you know how to differentiate a constant

Yes ofc! I just wanted to know if we needed to or not

 

[pka]

Instead of trying to work out the integral, I would take the derivative of each choice ...

Yes ofc! I just wanted to know if we needed to or not

If [imath]f(x)[/imath] is a differentiable function and [imath]{\displaystyle y = \int_1^{f(x)} {g(t)dt} \text{ then } \frac{{dy}}{{dx}} = \left( {g(f(x))} \right)f'(x)}[/imath]
[imath][/imath][imath][/imath][imath][/imath]