Question #eab38 Calculus Introduction to Integration Definite and indefinite integrals 1 Answer Alberto P. Nov 11, 2016 6(x^(7/6)/7-x^(5/6)/5+x^(1/2)/3-x^(1/6)+arctanx^(1/6))+c6(x767−x565+x123−x16+arctanx16)+c Explanation: Use z=x^(1/6)\ \ => x=z^6, sqrt(x)=z^3, root(3)(x)=z^2, dx=6z^5dz intsqrtx/(1+root(3)x)dx=6intz^8/(1+z^2)dz Then z^8/(1+z^2)=z^6-z^4+z^2-1+1/(a+z^2) so intsqrtx/(1+root(3)x)dx=6(z^7/7-z^5/5+z^3/3-z+arctan z)+c then make substitution z=x^(1/6) 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 2683 views around the world You can reuse this answer Creative Commons License