How do you find the integral of 0 to the infinity of #x^(8/3) dx#? Calculus Introduction to Integration Basic Properties of Definite Integrals 1 Answer Jim H Apr 10, 2015 #int_0^oo x^(8/3) dx = lim_(brarroo) int_0^b x^(8/3) dx# #=lim_(b rarr oo) 3/11 x^(11/3)]_0^b = lim_(brarroo)3/11 b^(11/3)=oo# The integral diverges. Answer link Related questions What are five basic properties of definite integrals? What is the integral of an integral? What is the integral of a quotient? How do I evaluate #int_0^5(2 e^x + 5cos(x)) dx#? Why can't you integrate #sqrt(1+(cosx/-sinx)^2#? What are the different strategies of integration? What is the integral from 0 to 4 of lnx dx? How do you evaluate the integral of #(ln x)^2 dx#? How do you find the integral of #abs(x) dx# on the interval [-2, 1]? Given f(x)=∫ (t^2−1)/(1+cos^2(t))dt At what value of x does the local max of f(x) occur ? (a=0... See all questions in Basic Properties of Definite Integrals Impact of this question 2489 views around the world You can reuse this answer Creative Commons License