How to integrate lnx by parts?
Integration by parts formula: ∫ udv/dx = uv - ∫ du/dxv dx
To solve this problem we need to use a trick by thinking of lnx as lnx1
So we can choose: u=lnx, dv/dx=1
The next step is to find du/dx and v.
du/dx=1/x As we have differentiated each side with respect to x
v=x By integrating each side with respect to x
Now we have all the required parts to use the integration by parts formula.
∫ lnx = lnxx – ∫ 1/x*x dx
= xlnx – ∫ 1 dx
= xlnx – x + c
RJ
Related Maths A Level answers
All answers ▸Show that r^2(r + 1)^2 - r^2(r - 1)^2 ≡ 4r^3.
Differentiate 7(3x^2+7)^(1/3)
Show that the equation 2sin^2(x) + 3sin(x) = 2cos(2x) + 3 can be written as 6sin^2(x)+3sin(x) - 5 = 0. Hence solve for 0 < x < 360 degrees. Giving your answers to 1.d.p.
The curve C has equation y = x^3 - 3x^2 - 9x + 14. Find the co-ordinates and nature of each of the stationery points of C.