Integrate cos(4x)+16x^3 with respect to x

This is a simple integration, integrating each individual term with respect to x.For the cos(4x), you should use 'integration by substitution' as it is a function of a function.cos(4x) = cos(u) and u = 4x where dx/du = 4, so dx = (1/4)duso we are now integrating: (1/4)cos(u) duthe 1/4 is a constant so can be taken infront---> integrates to sin(u)The integration of cos(u) is sin(u), using the memorised circle that can be used below:Down is differentiation, up is integration sinxcosx -sinx-cosx (then back to sinx and repeat)so (sin(u))/4and u = 4x so answer is sin(4x)/4Integrating the second value, by adding a power then dividing by the new power:16x^3 becomes (16x^4)/4 = 4x^4So finally, the solution is:sin(4x)/4+ 4x^4+Constant

AC
Answered by Aadil C. Maths tutor

3152 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A curve is defined by the parametric equations x = 2t and y = 4t^2 + t. Find the gradient of the curve when t = 4


A ball is thrown vertically upwards with a speed of 24.5m/s. For how long is the ball higher than 29.4m above its initial position? Take acceleration due to gravity to be 9.8m/s^2.


Use the geometric series formula to find the 9th term in this progression : 12 18 27...


A curve has equation x^2 + 2xy – 3y^2 + 16 = 0. Find the coordinates of the points on the curve where dy/dx =0


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