Thread: need help with partial fraction

1. need help with partial fraction

So we are having a holiday right now and I decide to go over the math which I'm bad at "partial fraction"

The question is my exercise book is $\displaystyle (x^3+3x+7)sin^2(y)\frac{dy}{dx}=x^2+1 for, y(-1)=0$

so I work around with the algebra a bit and got the equation to become

$\displaystyle \int sin^2(y)dy=\int\frac{x^2+1}{x^3+3x+7}dx$

the problem is that I wasn't sure how to integrate $\displaystyle \frac{x^2+1}{x^3+3x+7}$ this since I cannot factorise the denominator into somethign like (x^2+A)(x+B)
so how does one set up $\displaystyle \frac{x^2+1}{x^3+3x+7}$ for partial fractions

Best Regards
Junks

2. Re: need help with partial fraction

see the derivative of denominator is 3x^2 + 3 = 3(x^2+1) Thus you can write
(x^2+1) / ( x^3 + 3x + 7 ) = 1/3 [ 3(x^2+1) + 7] /( x^3 + 3x + 7 )
But still I observe that you will have a problem integrating 7 / ( x^3 + 3x + 7 )

3. Re: need help with partial fraction

Originally Posted by junkwisch
So we are having a holiday right now and I decide to go over the math which I'm bad at "partial fraction"

The question is my exercise book is $\displaystyle (x^3+3x+7)sin^2(y)\frac{dy}{dx}=x^2+1 for, y(-1)=0$

so I work around with the algebra a bit and got the equation to become

$\displaystyle \int sin^2(y)dy=\int\frac{x^2+1}{x^3+3x+7}dx$

the problem is that I wasn't sure how to integrate $\displaystyle \frac{x^2+1}{x^3+3x+7}$ this since I cannot factorise the denominator into somethign like (x^2+A)(x+B)
so how does one set up $\displaystyle \frac{x^2+1}{x^3+3x+7}$ for partial fractions

Best Regards
Junks
One probably wouldn't set it up for partial fractions. One would probably use $\displaystyle u$ substitution.

4. Re: need help with partial fraction

Originally Posted by SlipEternal
One probably wouldn't set it up for partial fractions. One would probably use $\displaystyle u$ substitution.
Thank you slipeternal

I felt really dumb right now