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

15187 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Solve the simultaneous equations y = x + 3, y^2 - x^2 + 3 = -6x


The element of a cone has length L. For what height H (with respect to L) will the volume of the cone be the largest?


Edexcel C1 2015 Q10. A curve with equation y = f (x) passes through the point (4, 9). Given that f′(x)=3x^(1/2)-9/(4x^(1/2))+2. Find f(x), giving each term in its simplest form.


How would you express (11+x-x^2)/[(x+1)(x-2)^2] in terms of partial fractions?


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 2013–2024

Terms & Conditions|Privacy Policy