# Math Help - integrate

1. ## integrate

How can integrate the following

$

dy/dx = ( 5x^3 + 7y + 5 )^2

$

2. Originally Posted by TGASJOOL
How can integrate the following

$

dy/dx = ( 5x^3 + 7y + 5 )^2

$
Expand the square on the right giving you a sixth order polynomial in x, then integrate term by term

CB

3. i forgot to mention

i should use a substitution

$
u = ( 5x^3 + 7y + 5 )
$

Please help.

4. Originally Posted by CaptainBlack
Expand the square on the right giving you a sixth order polynomial in x, then integrate term by term

CB
Since there is a term with y in it on the right hand side, it's possible that the real question is not to integrate but to solve a differential equation. The OP will need to clarify the situation.

Originally Posted by TGASJOOL
i forgot to mention

i should use a substitution

$u = ( 5x^3 + 7y + 5)$

Please help.
See my remark above.

5. Originally Posted by TGASJOOL
i forgot to mention

i should use a substitution

$
u = ( 5x^3 + 7y + 5 )
$

Please help.
In which case differentiate then you have:

$\dfrac{du}{dx}=15x^2+7\dfrac{dy}{dx}=15x^2+7u^2$

or:

$\dfrac{du}{dx}-7u^2=15x^2$

which you need to solve

CB

6. Originally Posted by TGASJOOL
i forgot to mention

i should use a substitution

$
u = ( 5x^3 + 7y + 5 )
$

Please help.
No, you shoudn't. Since there is no "du" already in the integrand, it is far easier to just multiply it out and integrate the polynomial as Captain Black first said.