Question

can someone help me to solbe this question.. INTEGRATE (4x-2)/(x^2+2x+10)

Answer 1

yes.. can u help me?

Answer 2

\[\int\limits\frac{ 4x-2 }{ x^2+2x+10 }dx=2 \int\limits \frac{ 2x-1 }{ x^2+2x+10 }dx=2\int\limits \frac{ 2x+2-3 }{ x^2+2x+10 }dx=I_1+I_2+C\]\[I_1=2\int\limits \frac{ 2x+2 }{ x^2+2x+10 }dx=2Ln \left( x^2+2x+10 \right)\]\[I_2=-6\int\limits \frac{ dx }{ x^2+2x+10 }=-6\int\limits \frac{ dx }{ (x+1)^2+9 }=-\frac{ 2 }{ 3 }\int\limits \frac{ dx }{ 1+(\frac{ x+1}{ 3 } )^2}\]\[I_2=-2Atan \left( \frac{ x+1 }{ 3 } \right)\]Your solution is:\[2Ln \left( x^2+2x+10 \right)-2Atan \left( \frac{ x+1 }{ 3 } \right)+C\]

Answer 3

@CarlosGP i can't read it..

Answer 4

Let´s see if you can read the attached file