Q. 32 - Calculus

Question

Use integration formulas to solve each integral in Exercises 21–62. You may have to use algebra, educated guess-and-check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating.  

$\int 4e^{2x-3}dx$

Step-by-Step Solution

Answer

The solution of the integral is $2e^{2x-3}+C.$

Step 1. Given Information.

The given integral is $\int 4e^{2x-3}dx.$

Step 2. Solve.

By solving the integral we get, 

$$\begin{gathered} \int 4e^{2x-3}dx \\ =4\int e^{2x-3}dx \\ =4\left(\frac{1}{2}\right)e^{2x-3}+C \\ =2e^{2x-3}+C \end{gathered}$$

Step 3. Verification.

To verify the answer we differentiate $2e^{2x-3}+C$ it.

On differentiating we get,

$$\begin{gathered} 2e^{2x-3}+C \\ =\frac{d}{dx}2e^{2x-3}+\frac{d}{dx}C \\ =2\left(2e^{2x-3}\right)+0 \\ =4e^{2x-3} \end{gathered}$$

Hence proved.