Question

integrate the function e^(2x + 3).dx

Answer 1

this is answer .........

Answer 2

$\bf{\int{e^{(2x+3)}}\,dx}$

let (2x + 3) = t ------(1)

differentiate both sides,
2.dx = dt => dx = 1/2 dt -----(2)

put equations (1) and (2) in I,

so, I = $\bf{\frac{1}{2}\int{e^t}\,dt}$

= $\bf{\frac{1}{2}e^t + C}$

put t = (2x + 3)

therefore, I = $\frac{1}{2}\bf{e^{(2x+3)}}+C$