Integrate using by parts twice : ∫e^(x)*(cos(x))dx

By putting u=cosx and v’= e^x , use the by parts formula to get:∫e^(x)(cos(x)) dx = cos(x)e^x - ∫-(e^x)sin(x) dx. Use by parts again on the second term to get ∫ =cos(x)e^x + sin(x)e^x - ∫e^(x)(cos(x))dx. The last term is the same integral as the one we have to solve. Take this to the other side to get: 2 ∫e^(x)(cos(x))dx = cos(x)e^x + sin(x)e^x which gives: ∫e^(x)(cos(x))dx = (e^x(cosx+sinx))/2 + Constant

IZ
Answered by Isma Z. Maths tutor

6105 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do we differentiate y=a^x when 'a' is an non zero real number


Differentiate the equation x^2 + 2y^2 = 4x


Given two coordinate points (a1,b1) and (a2,b2), how do I find the equation of the straight line between them?


The line AB has equation 3x + 5y = 7, find; a) the gradient of AB b) the x-axis and y-axis intercepts c) sketch the graph


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences