# The graph of a function f is shown.? Use the differential equation and the given point to find an equation of the function dy/dx = 4x+ (9x^2) / ( (3x^3 +1) ^3/2 )...

The graph of a function f is shown.?

Use the differential equation and the given point to find an equation of the function

dy/dx = 4x+ (9x^2) / ( (3x^3 +1) ^3/2 )

http://www.webassign.net/larcalc9/4-5-090.gif

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You need to find the function using the process of integration such that:

`int dy = int (4x+ (9x^2)/((3x^3 +1)^(3/2))) dx`

Using the property of linearity of integral yields:

`y = int 4x dx + int (9x^2)/((3x^3 +1)^(3/2))) dx`

`y = 4x^2/2 + int (9x^2)/((3x^3 +1)^(3/2))) dx`

You need to solve the integral `int (9x^2)/((3x^3 +1)^(3/2))) dx ` using the following substitution such that:

`3x^3 + 1 = t => 9x^2...

(The entire section contains 192 words.)