PROGRAM series15
!
! Author:  Br. David Carlson
!
! Date:  December 31, 1999
!
! Revised:  May 2, 2004; April 18, 2016
!
! This program uses power series to find an approximate value for the
! integral of ln(x + 1) from 1/4 to 3/4.  Compare with the output of integ3.f90.
! This is a quick solution using a sequence of assignment statements, which can
! be faster to write than finding the pattern needed to do the same calculations
! in a loop.

IMPLICIT NONE

REAL::x, xsquared, top, sum1, sum2

WRITE (*, 20)
20 FORMAT (1X, 'Program to integrate ln(x + 1) from 1/4 to 3/4 using series')

x = 0.75
xsquared = x * x
sum1 = 0.0

top = xsquared
sum1 = sum1 + top / 2.0
top = top * x
sum1 = sum1 - top / 6.0
top = top * x
sum1 = sum1 + top / 12.0
top = top * x
sum1 = sum1 - top / 20.0
top = top * x
sum1 = sum1 + top / 30.0
top = top * x
sum1 = sum1 - top / 42.0
top = top * x
sum1 = sum1 + top / 56.0
top = top * x
sum1 = sum1 - top / 72.0
top = top * x
sum1 = sum1 + top / 90.0
top = top * x
sum1 = sum1 - top / 110.0

x = 0.25
xsquared = x * x
sum2 = 0.0

top = xsquared
sum2 = sum2 + top / 2.0
top = top * x
sum2 = sum2 - top / 6.0
top = top * x
sum2 = sum2 + top / 12.0
top = top * x
sum2 = sum2 - top / 20.0
top = top * x
sum2 = sum2 + top / 30.0
top = top * x
sum2 = sum2 - top / 42.0
top = top * x
sum2 = sum2 + top / 56.0
top = top * x
sum2 = sum2 - top / 72.0
top = top * x
sum2 = sum2 + top / 90.0
top = top * x
sum2 = sum2 - top / 110.0

WRITE (*, 200) sum1 - sum2
200 FORMAT (1X, 'The approximate value is ', E16.7)

END PROGRAM