Question #59c28
1 Answer
Mar 13, 2017
Rewrite the numerator:
#int_2^4(x^2+1)/(x-1)dx=int_2^4(x(x-1)+(x-1)+2)/(x-1)dx#
#color(white)(int_2^4(x^2+1)/(x-1)dx)=int_2^4(x+1+2/(x-1))dx#
#color(white)(int_2^4(x^2+1)/(x-1)dx)=[x^2/2+x+2ln(abs(x-1))]_2^4#
Evaluating gives:
#int_2^4(x^2+1)/(x-1)dx=(8+4+2ln3)-(2+2+2ln1)#
#color(white)(int_2^4(x^2+1)/(x-1)dx)=8+2ln3#
