How do you solve integrals which are the result of a chain rule e.g. the integral of sin(2x+1)

∫sin(2x + 1)dx[newline]In this case the easiest way to solve the integral is to perform a substitution. The substitution should reduce the integral to something you can solve. In this case we will[newline]let u = 2x + 1[newline]This allows the integral to be written as[newline]∫sin(u)dx[newline]We are not done yet as there is still the dx to deal with. The next step is to differentiate u[newline]du/dx = 2[newline]We can then rearrange this equation to get a substitution for dx[newline]dx = du/2[newline]Subbing this into the integral gives[newline]1/2 ∫sin(u)du[newline]Which can be solved using the standard integral on the formula sheet to give[newline]-1/2 cos(u) + C[newline]All that is left to do now is replace u with 2x + 1 giving the answer[newline]∫sin(2x + 1) = -1/2 cos(2x + 1) + C

Related Maths Scottish Highers answers

All answers ▸

Calculate the rate of change of y(t) = 1/(4t), when t = 8


Why is the gradient of a curve at a point the same as the gradient of the tangent if you can't use gradient formula on a curve?


Show that the two vectors A= 2i+3j-k and B=3i-j+3k are perpendicular


Find an equation for the straight line AB , giving your answer in the form px+qy=r, where p, q and r are integers. Given that A has co-ordinates (-2,4) and B has co-ordinates (8,-6)


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