Integrate a^x with respect to x

This comes up in C4 in A level maths and differentiating it could come up in C3. You can write a^x as exp(ln(a^x))=exp(xln(a)) then differentiating this, you get ln(a)exp(xln(a))=ln(a)a^x. By differentiating you can recognise the integral will be (a^x)/ln(a) +c or you can perform a u substitution where u=a^x then du=ln(a)a^xdx. dx=1/ln(a) * 1/u * du. Therefore the integral is now u/(u*ln(a)) du = 1/ln(a) du = u/ln(a) +c = a^x/ln(a) +c.

I have picked this since it could come up in C3 and C4 and I have had the same question asked to me by my peers before. The working can be further expanded by explaining how a^x can be written in terms of e and the natural logarithm, with these being inverse functions of each other, a topic within C3.

Answered by John W. Maths tutor

30354 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A straight line passes through the point (2,1) and has a gradient of 3. Find the co-ordinates of the points where this line intersects the axes


How do I integrate x/(x^2 + 3) ?


Use logarithms to solve the equation 3^(2x+1) = 4^100


A curve C has equation y=(2x-3)^5. Find the equation of the normal of this curve at point P with y coordinate -32.


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