Question

Find the anti derivative of e^2x+3​

Answer 1

Check the attachment_______♡

Answer 2

Answer

• ¹/₂ e²ˣ⁺³ + c

Given

• e²ˣ⁺³

To Find

• Anti-derivate of given value

Solution

$\rm \int e^{2x+3}\ dx$

$\boxed{\begin{minipage}{3cm} \rm Let\ , u=2x+3\\\\\implies \rm du=2dx\\\\\implies \rm dx=\dfrac{du}{2}\end{minipage}}$

$\implies \rm \int e^u\ \dfrac{du}{2}\\\\\implies \rm \dfrac{1}{2}\int e^u\ du\\\\\implies \rm \dfrac{1}{2}\ e^u\ +c\\\\\implies \rm \dfrac{1}{2}\ e^{2x+3}+c$