Integrate ln(x) with respect to x.
Here we can use integration by parts. Notice that ln(x) can be written as ln(x)1, so we can integrate 1 and differentiate ln(x).
Then using the formula int(uv') dx = uv - int(u'v) dx, we find that the integral of ln(x) is xln(x) - int(1/x * x) dx = xln(x) - int(1) dx = xln(x) - x + c, where c is a constant of integration.
TW
Answered by Tim W. • Further Mathematics tutor
4587 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸How to determine the modulus of a complex number?
Does the following matrix A = (2 2 // 3 9) (upper row then lower row) have an inverse? If the matrix A^2 is applied as a transformation to a triangle T, by what factor will the area of the triangle change under the transformation?
Integrate x^2sin(x) between -pi and pi
Using graphs, show how the Taylor expansion can be used to approximate a trigonometric function.