Integrate $$\int xe^x \mathop{\mathrm{d}x}$$.

We use integration by parts. Set $u = x$ and $dv/dx = e^x$. This leads to $du/dx = 1$, and $v = e^x$. Then:\begin{align*}\int xe^x \mathop{\mathrm{d}x} &= xe^x - \int e^x \mathop{\mathrm{d}x}\&= xe^x - e^x.\end{align*}

Answered by Christopher N. Maths tutor

3552 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

proof for the derivative of sin(x) is cos(x) (5 marks)


What is integration?


A line L is parallel to y=4x+5 and passes through the point (-1, 6). Find the equation of the line L in the form y=ax+b . Find also the coordinates of its intersections with the axes.


Find the Co-ordinates and nature of all stationary points on the curve y=x^3 - 27x, and attempt to sketch the curve


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