Question

Integral question for you!

Answer 1

\[\int\limits_{}^{}\frac{ x ^{3}+2x ^{2}+x-7 }{ x ^{2}+x-2 }dx\]

Answer 2

Could i use polynomdivision and get
\[\int\limits_{}^{}(x+1-\frac{ 2x-5 }{ x ^{2}+x-2})dx\]

Answer 3

If so, how do I go about solving the fraction in the integral?

Answer 4

We could ummmm....\[\Large \int\limits x+1-\frac{ 2x\color{#CC0033}{+1-1}-5 }{ x ^{2}+x-2} dx\]No no no never mind that little trick will confuse you probably :o
Let's just jump right into a trig sub.
So we need to complete the square in the denominator.\[\Large \int\limits x+1-\frac{ 2x-5 }{ x^2+x\color{#CC0033}{+\frac{1}{4}-\frac{1}{4}}-2}dx\]You have learned Trig Substitution, yes? :o

Answer 5

\[\Large \int\limits\limits x+1-\frac{ 2x-5 }{ \left(x+\frac{1}{2}\right)^2-\frac{9}{4}}dx\]

Answer 6

Hm, ok, I'll try that in the morning! Thank you! :)