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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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 $e^{2x+3}$.

Similar Questions

Find: $\int \sin^{3} x \, dx$

Write an anti-derivative for the following function using the method of inspection: $\frac{1}{x}, x \neq 0$

The value of $\int \frac{dx}{x\sqrt{x^4 - 1}}$ is

$\int \frac{2x}{(2x + 1)^2} dx = $

$\int \frac{x - 2}{x^2 - 4x + 3} dx = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module