(b)\int (x^(2)+3x-1)/(x(x+1)(x^(2)+1))dx (c)\int (e^(2x))/(e^(2x)+3e^(x)+2)dx (d)\int e^(x)sin(x)dx Consider a continuous function f:R->R such that f(1)=3,f(2)=5,f(4)=-1, and \int_1^2 f(x)dx=3(a) Use the method of substitution to evaluate \int_1^2 xf^(')(x^(2))dx (b) Use integration by parts to evaluate \int_1^2 xf^(')(x)dx An epidemic is growing in a region according to the rate N^(')(t)=(100t)/(t^(2)+2) where N(t) is the number of people infected after t days. (a) Find a formula for the number of people infected after t days, given that 37 people were infected at t=0.(b) Use your answer from part (a) to find the number of people infected after 21 days.