calculus???

Question

integrate this: lnx.dx i know the answer is (xlnx-x). but pls show how!

Answer 1

u hav to do it by "integration by parts" method

first the formula is

int: u dv = uv - int: v du

now about choosing u & v :


choose u by the following priority

LIATE
L - logarithmic functions
I - inverse trignometric fn.
A - algebraic fn.
T - trigonometric fn.
E - exponential fn.

(some tell the priority as ILATE)

so if you have x sinx dx

you choose u =x
&
dv = sinx dx


here in this case you have only one fn.
so take

u = ln x

differentiating

du = 1/x dx

&
take

v= dx

integrating

v= x

now using the formula

int ln x dx = x ln x - int : x / x dx

= x ln x - int: dx

= x ln x - x

Answer 2

There is a "trick" involved in this solution.

The "trick" is to multiply by 1.

Consider the integral I = ∫ lnX .1 dX

Integrate by parts where;-

u = log X and dv/dX = 1

du / dX = 1/X and v = X

I = ln X . X - ∫ X. 1/X dX

I = ln X . X - ∫ 1 dX

I = X ln X - X + C which is required answer.

Answer 3

I believe it is integration by parts(from the answer, it appears that way)
let u=___ and dv= ___ dx, from there you find du=______dx and v=______.

Plug the numbers into the following.
uv-(the integral of)v du

do the integral of v du, and you've go the answer.


If you have a text book, look up inegration by parts, I am sure it explains this in more detail and is much more clear.

Answer 4

i'd say structure is area of engineering which signifies that an effective draw close on math is major, pre-cal is is like algebra to the subsequent aspect with the Pi chart and understanding about radians and perspective measures (which looks major) yet Calculus is the learn of derivatives, (the slope of a line at a particular aspect) type of unnecessary no count number what container of workd your going to, in case you question me.

Answer 5

you need to integrate by parts.

int lnx d/dx(x) dx
= xlnx - int x * 1/x .dx
= xlnx - int 1 dx
= xlnx - x + C

Answer 6

let y = ln(x) therefore dy = (1/x)dx so dx = xdy = exp(y)dy

so we have INT(ln(x)dx) = INT(yexp(y)dy)
Now use integration by part and solve