How do you find the definite integral for: #(2+3x) / (4+x2) dx# for the intervals #[0, 1]#? Calculus Introduction to Integration Formal Definition of the Definite Integral 1 Answer Ratnaker Mehta Nov 23, 2017 # arc tan(1/2)+3/2ln(5/4).# Explanation: Suppose that, #I=int_0^1(2+3x)/(4+x^2)dx.# #:. I=int_0^1 2/(4+x^2)dx+int_0^1(3x)/(4+x^2)dx,# #=2int_0^1 1/(2^2+x^2)dx+3/2int_0^1 (2x)/(4+x^2)dx,# #=2[1/2*arc tan(x/2)]_0^1+3/2int_0^1 {d/dx(4+x^2)}/(4+x^2)dx,# #=[arc tan(1/2)-arc tan(0)]+3/2[ln(4+x^2)]_0^1,# #=arc tan(1/2)-0+3/2[ln(4+1^2)-ln(4+0^2)],# #=arc tan(1/2)+3/2(ln5-ln4),# #=arc tan(1/2)+3/2ln(5/4).# Answer link Related questions What is the Formal Definition of the Definite Integral of the function #y=f(x)# over the... How do you use the definition of the definite integral? What is the integral of dy/dx? What is an improper integral? How do you calculate the double integral of #(xcos(x+y))dr# where r is the region: 0 less than... How do you apply the evaluation theorem to evaluate the integral #3t dt# over the interval [0,3]? What is the difference between an antiderivative and an integral? How do you integrate #3x^2-5x+9# from 0 to 7? Question #f27d5 How do you evaluate the definite integral #int sqrtt ln(t)dt# from 2 to 1? See all questions in Formal Definition of the Definite Integral Impact of this question 1393 views around the world You can reuse this answer Creative Commons License