Question

Integrate 2x+3/((x-2)(x^2+3))

Answer 1

gonna have to do partial fractions i think, this may take a while, but i'll try

Answer 2

Thank you I'm taking an exam right now please help

Answer 3

2x+3/((x-2)(x^2+3))=A/(x-2)+(Bx+C)/(x^2+3)
2x+3=A(x^2+3)+(Bx+C)(x-2)
=Ax^2+3A+Bx^2-2Bx+Cx-2C
=(A+B)x^2+(-2Bx+C)x+(3A-2C)=2x+3
setting coefficients equal:
A +B =0
-2B+C=2
3A -2C=3
Solve the system to get A=1, B=-1, C=0
so now our integral is, just wait...

Answer 4

\[\int\limits1/(x+2)-x/(x^2+3)dx=\ln (x+2)-(1/2)\ln (x^2+3)+C\]

Answer 5

actually it should have absolute value signs:
\[\ln \left| x+2 \right|-(1/2)\ln \left| x^2+3 \right|+C\]