Question

Differentiation of this question if dont know no need to comment

Answer 1

integral from x1 to x2 of 1/(2x+3) dx

$I=\int \limits_{x_1}^{x_2} {\frac{1}{2x+3}} \, dx\\\\=\frac{1}{2} \int \limits_{x_1}^{x_2} \frac{1}{x+3/2} \, dx \\\\=\frac{1}{2} [ Ln(x+3/2) ]_{x_1}^{x_2}\\\\=\frac{1}{2} Ln [\frac{x_2+1.5}{x_1+1.5} ]$

Answer 2

$\displaystyle \int\limits_{ x_{4} }^{ x_{2} } \frac{1}{2x + 3} \, dx \\ \\ = \displaystyle \int\limits_{ x_{4} }^{ x_{2} } \frac{1}{2(x + \frac{3}{2}) } \, dx \\ \\ = \frac{1}{2} \displaystyle \int\limits_{ x_{4} }^{ x_{2} } \frac{1}{(x + \frac{3}{2}) } \, dx \\ \\ = \frac{1}{2} {( log(x + 1.5) )}^{ x_{2} } _{x_{4}}$