Definite Integral of a Rational Function

Given six numbers: a, b, c, d, L, and R, compute the definite integral:

$$\int_{L}^{R}\frac{cx+d}{ax+b}\,dx$$

Round the result to 6 decimal places. It is guaranteed that during the calculation the denominator ax+b is never 0 and the integral converges. When a ≠ 0 you may use the following antiderivative formula:

$$F(x)=\frac{c}{a}x+\frac{d-\frac{c\,b}{a}}{a}\ln|ax+b|+C$$

If a = 0, the integrand becomes a linear function and should be integrated directly.

inputFormat

The input consists of a single line with 6 space-separated numbers: a b c d L R.

outputFormat

Output the value of the integral computed to 6 decimal places.

sample

1 0 1 0 0 1

1.000000