Find the integral of a^(x) where a is a constant

Starting with ∫ax dx ,
We can re-write ax using logs as eln(a)*x using some of their properties
We use the substitution u = ln(a)*x (as such du/dx = ln(a)) allowing us to easily integrate eu  with respect to u, by substituting du/ln(a) in the place of dx
The result is eu/ln(a) + c and after re-writing in terms of x by we get an answer of:
ax/ln(a) +c

Answered by Andreas P. Maths tutor

2943 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the values of x, where 0 < x < 360, such that x solves the equation: 8(tan[x])^2 – 5(sec[x])^2 = 7 + 4sec[x]


Find the values of x for which f(x) is an increasing function given that f(x)=8x-2x^2


Find the gradient of the curve (x^3)-4(y^2)=12xy at the point P(-8,8)


A curve has an equation: (2x^2)*y +2x + 4y – cos(pi*y) = 17. Find dy/dx


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences