How do you integrate ((ln(x))^7)/x dx? Calculus Techniques of Integration Integration by Substitution 1 Answer Tazwar Sikder Mar 14, 2018 frac(1)(8) (ln(x))^(8) + C Explanation: We have: int frac((ln(x))^(7))(x) dx = int (ln(x))^(7) cdot frac(1)(x) dx Let u = ln(x) Rightarrow du = frac(1)(x) dx: = int u^(7) du = frac(u^(7 + 1))(7 + 1) + C = frac(1)(8) u^(8) + C Replace u with ln(x): = frac(1)(8) (ln(x))^(8) + C Answer link Related questions What is Integration by Substitution? How is integration by substitution related to the chain rule? How do you know When to use integration by substitution? How do you use Integration by Substitution to find intx^2*sqrt(x^3+1)dx? How do you use Integration by Substitution to find intdx/(1-6x)^4dx? How do you use Integration by Substitution to find intcos^3(x)*sin(x)dx? How do you use Integration by Substitution to find intx*sin(x^2)dx? How do you use Integration by Substitution to find intdx/(5-3x)? How do you use Integration by Substitution to find intx/(x^2+1)dx? How do you use Integration by Substitution to find inte^x*cos(e^x)dx? See all questions in Integration by Substitution Impact of this question 8811 views around the world You can reuse this answer Creative Commons License