Differentiate: f(x)=(ax^2 + bx + c) ln(x + (1+x^2)^(1/2)) + (dx + e) (1 + x^2)^(1/2). Hence integrate i) ln(x + (1 + x^2)^(1/2)), ii) (1 + x^2)^(1/2), iii) x ln(x + (1 + x^2)^(1/2)).

Differentiate equation: f'(x) = (2ax + b) ln(x + (1+x^2)^(1/2)) + ((a + 2d)x^2 + (b + c)x + (c+d)) (1 + x^2)^(-1/2).

Select correct values for constants to get:

i) x ln(x + (1+x^2)^(1/2)) - (1 + x^2)^(1/2) + C

ii) 1/2 ln(x + (1+x^2)^(1/2)) + x/2 (1 + x^2)^(1/2) + C

iii) ((x^2)/2 + 1/4) ln(x + (1+x^2)^(1/2)) - x/4 (1 + x^2)^(1/2) + C

ME
Answered by Morgan E. STEP tutor

3291 Views

See similar STEP University tutors

Related STEP University answers

All answers ▸

How would you prove the 'integration by parts' rule?


Given a differential equation (*), show that the solution curve is either a straight line or a parabola and find the equations of these curves.


Let p and q be different primes greater than 2. Prove that pq can be written as difference of two squares in exactly two different ways.


Show that substituting y = xv, where v is a function of x, in the differential equation "xy(dy/dx) + y^2 − 2x^2 = 0" (with x is not equal to 0) leads to the differential equation "xv(dv/dx) + 2v^2 − 2 = 0"


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