How can I integrate e^x sinx?

Such an integral looks difficult to manage; clearly it is a case of integration by parts, but neither part of the product appears to reduce easily into a nicer form.

The key here is use the fact that sinx has a cyclic pattern when it is repatedley differentiated. Keeping our orignal integral on the left hand side, after two applications of integration by parts, where sinx is the term to be differentiated, we obtain a second intance of the integral on the right hand side of the equation. Moving this integral to the left hand side with our original integral and dividing the equation by two, we acquire the required result.

AW
Answered by Alex W. Maths tutor

5675 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the area enclosed between the curves y = f(x) and y = g(x)


Differentiate 8x^4 + 2x^2 + 10


A curve has parametric equations x=2t, y=t^2. Find the Cartesian equation of the curve.


Solve x^2 + 8x +3 = 0 by completing the square.


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