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Chapter 4: Q. 49 (page 362)

Use integration formulas to solve each integral in Exercises 21鈥�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. (Hint for Exercise 54: tanx=sinxcosx).

鈭�e3x-2e4xe2xdx.

Short Answer

Expert verified

The value of the given integral will beex-e2x+c.

Step by step solution

01

Step 1. Given Information.

Given the integral:鈭�e3x-2e4xe2xdx.

02

Step 2. Formula involved.

鈭�exdx=ex+c.and鈭�eaxdx=eaxa+c,whereaisaconstant.

03

Step 3. Solving the integral.

鈭�e3x-2e4xe2xdx=鈭�(e3x-2x-2e4x-2x)dx=鈭�(ex-2e2x)dx=鈭�exdx-鈭�2e2xdx=ex-2e2x2+c=ex-e2x+c.

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