How do you integrate #f(x)=3^(5x-1)/e^(4x)# using the quotient rule? Calculus Basic Differentiation Rules Quotient Rule 1 Answer Andrea S. Mar 31, 2017 #int 3^(5x-1)/e^(4x) dx = 3^(5x-1)/(e^(4x)(5ln3-4))+C# Explanation: Note that: #3^(5x-1)/e^(4x) = (e^(ln3))^(5x-1)*e^(-4x) = e^((5ln3 -4)x)*e^(-ln3) = 1/3 e^((5ln3 -4)x# So: #int 3^(5x-1)/e^(4x) dx = 1/3 int e^((5ln3 -4)x)dx = e^((5ln3 -4)x)/(3(5ln3-4))+C = 3^(5x-1)/(e^(4x)(5ln3-4))+C# Answer link Related questions What is the Quotient Rule for derivatives? How do I use the quotient rule to find the derivative? How do you prove the quotient rule? How do you use the quotient rule to differentiate #y=(2x^4-3x)/(4x-1)#? How do you use the quotient rule to differentiate #y=cos(x)/ln(x)#? How do you use the quotient rule to find the derivative of #y=tan(x)# ? How do you use the quotient rule to find the derivative of #y=x/(x^2+1)# ? How do you use the quotient rule to find the derivative of #y=(e^x+1)/(e^x-1)# ? How do you use the quotient rule to find the derivative of #y=(x-sqrt(x))/(x^(1/3))# ? How do you use the quotient rule to find the derivative of #y=x/(3+e^x)# ? See all questions in Quotient Rule Impact of this question 1211 views around the world You can reuse this answer Creative Commons License