Using substitution, integrate x(2 + x))^1/2 where u^2 = 2 + x

u2 = 2 + xx = u2 - 2dx/du = 2u
ʃ x(2 + x))1/2 dx= ʃ xu dx= ʃ u(u2 - 2) dx= ʃ 2u2 (u2 - 2) du= ʃ 2u4 - 4u2 du= [2/5u5 - 4/3u3 + C]= 2/5 (2 + x)5/2 - 4/3 (2 + x)3/2 + C

SP
Answered by Sonali P. Maths tutor

3998 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Integrate the following expression with respect to x by parts: (2*x)*sin(x)


How to differentiate x^2 + y^2 - 2x + 6y = 5


Solve for 0<x≤2π, cos^2(x)-3cos(x)=5sin^2(x)-2, giving all answers exactly


Find the turning points of the curve y = x^3 +5x^2 -6x +4


We're here to help

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

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning