Question

Use substitution to convert the integral to an integral of a rational function. Then use partial fractions to evaluate the integral.\\ $\int \frac{(25e^x + 8)e^x}{(5e^x + 2)(5e^x + 4)} dx = $ ______ $+C$

          Use substitution to convert the integral to an integral of a rational function. Then use partial fractions to evaluate the integral.\\
$\int \frac{(25e^x + 8)e^x}{(5e^x + 2)(5e^x + 4)} dx = $ ______ $+C$

$Use substitution to convert the integral to an integral of a rational function. Then use partial fractions to evaluate the integral. ∫((25e^x + 8)e^x)/((5e^x + 2)(5e^x + 4)) dx = +C$

Added by Carlos M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

02/27/2023

Step 1

Then du = 5e dx, and we can rewrite the integral as: ∫ (25ex+8)ex dx = (1/5) ∫ (5ex+2) du Show more…

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Use substitution to convert the integral to an integral of a rational function. Then use partial fractions to evaluate the integral. (25ex+8)ex (5ex+2)(5ex+4)