Integrate the function e^{2x+3}. | vedclass

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Question

(A) Let $I = \int e^{2x+3} dx$.Substitute $t = 2x+3$.Then,$dt = 2 dx$,which implies $dx = \frac{1}{2} dt$.Substituting these into the integral:$I = \i

Vedclass · Accepted Answer

$\frac{1}{2}e^{2x+3} + C$

Vedclass · Answer

(A) Let $I = \int e^{2x+3} dx$.Substitute $t = 2x+3$.Then,$dt = 2 dx$,which implies $dx = \frac{1}{2} dt$.Substituting these into the integral:$I = \int e^t \cdot \frac{1}{2} dt$$I = \frac{1}{2} \int e^t dt$$I = \frac{1}{2} e^t + C$Substituting back $t = 2x+3$:$I = \frac{1}{2} e^{2x+3} + C$,where $C$ is an arbitrary constant.

Integrate the function $e^{2x+3}$.

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