Math Problem

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Machaira

Junior Contributor
Joined
Aug 19, 2002
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Abingdon, MD
Cookies are riding on the first solution to this:

∫(12x+8)(3x^2+4x)

It's been about 20 years since I've done anything like this and I've pretty much forgotten all my advanced math. I'd be lucky to solve for x. :)
 
Machaira said:
Cookies are riding on the first solution to this:

∫(12x+8)(3x^2+4x)

It's been about 20 years since I've done anything like this and I've pretty much forgotten all my advanced math. I'd be lucky to solve for x. :)
Click to expand...
I believe it is:

[ (x^2) (9x^2+22x+16) ]+C
 
Damn. . . I Love math. . . I hate arithmetic. . . .


check:

given that

∫ Ax^n = A ((x^n+1)/(n+1)) + C

and

∫ ( f(x) + g(x) ) = ∫ f(x) + ∫ g(x)

therefore

∫ (12x+8)(3x^2+4x) =
∫ (36 x^3 +24x^2 +48x^2 + 32x) =
∫ 36 x^3 + ∫ 72x^2 + ∫ 32x =

36 (x^4)/4 + 72(x^3) / 3 + 32 (x^2) / 2 =

9 x^4 + 24x^3 + 16 x^2 =

(x^2) ( 9x^2 + 24x + 16) =

(x^2) ( 9x^2 + 24x + 16) + C =

(x^2) (3x +4) ^2 +C

===========================

∫ (12x+8)(3x^2+4x) = (x^2) (3x +4) ^2 +C

Now - thats my final answer!!!!
 
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