How do you evaluate the integral of #int (2 -1/x)dx# from 1/2 to 3? Calculus Introduction to Integration Definite and indefinite integrals 1 Answer Andrea S. May 11, 2018 #int_(1/2)^3 (2-1/x)dx =5 - ln6# Explanation: Using the linearity of the integral: #int_(1/2)^3 (2-1/x)dx = 2int_(1/2)^3dx - int_(1/2)^3 dx/x# #int_(1/2)^3 (2-1/x)dx = 2(3-1/2) - (ln3-ln(1/2))# #int_(1/2)^3 (2-1/x)dx =5 - ln6# Answer link Related questions What is the difference between definite and indefinite integrals? What is the integral of #ln(7x)#? Is f(x)=x^3 the only possible antiderivative of f(x)=3x^2? If not, why not? How do you find the integral of #x^2-6x+5# from the interval [0,3]? What is a double integral? What is an iterated integral? How do you evaluate the integral #1/(sqrt(49-x^2))# from 0 to #7sqrt(3/2)#? How do you integrate #f(x)=intsin(e^t)dt# between 4 to #x^2#? How do you determine the indefinite integrals? How do you integrate #x^2sqrt(x^(4)+5)#? See all questions in Definite and indefinite integrals Impact of this question 2310 views around the world You can reuse this answer Creative Commons License