How do you evaluate the definite integral #int logx dx# from #[2,4]#? Calculus Introduction to Integration Definite and indefinite integrals 1 Answer F. Javier B. Apr 30, 2018 #I=6log2-2/ln10#. See details below Explanation: #I=intlogxdx# Lets do it by parts #u=logx# and #dv=dx# With this we have #du=1/(xln10)dx# and #v=x# #I=xlogx-int1/ln10dx=xlogx-1/ln10x=F(x)# #F(4)-F(2)=4log4-4/(ln10)-2log2+2/ln10=4log4-2log2-2/ln10=4log2^2-2log2-2/ln10=6log2-2/ln10# 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 3918 views around the world You can reuse this answer Creative Commons License