Showing all your working, evaluate ∫(21x^6 - e^2x- (1/x) +6)dx

 ∫(21x6-e2x-1/x+6)dx

To tackle this question, I would do each part separately.

Firstly, take 21x6...using the product rule this intergrates like so (21/(6+1))x6+1 = (21/7)x7 = 3x7

Second, ekx always intergrates to (1/k)ekx .........so -e2x goes to (-1/2)e2x.

1/x has the common intergral of lnx which must simply be learnt.

And finally, 6 intergrates to 6x.

We then collect all these parts and put them together so we get y=3x7-(1/2)e2x-lnx+6x+C

Always remember that for intergration without limits you must always add C at the end.

DG
Answered by David G. Maths tutor

6708 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A curve has the equation 2x^2 + xy - y^2 +18 = 0. (1) Find the coordinates of the points where the tangent to the curve is parallel to the x-axis.


What is the area under the graph of (x^2)*sin(x) between 0 and pi


Find the values of A between and including 0 and 360 degrees for tan(2A) = 3tan(A)


The equation of a line is y=e(^2x)-9 and the line has points at (0,a) and (b,0). Find the values of a and b.


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