Question

Make a substitution to express the integrand as a rational function and then evaluate the integral. (Use C for the constant of integration.) ∫(3e^2x)/(e^2x + 15ex + 54) dx

Name: make a substitution to express the integrand as a rational function and then evaluate the integral use c for the constant of integration 3e2x e2x 15ex 54 dx 84304
Uploaded: 2023-08-01T00:03:15-08:00
Duration: 2 min 42 s
Channel: Supreeta N
Description: make a substitution to express the integrand as a rational function and then evaluate the integral use c for the constant of integration 3e2x e2x 15ex 54 dx 84304

          Make a substitution to express the integrand as a rational function and then evaluate the integral.
(Use C for the constant of integration.)
∫(3e^2x)/(e^2x + 15ex + 54) dx

make a substitution to express the integrand as a rational function and then evaluate the integral use c for the constant of integration 3e2x e2x 15ex 54 dx 84304

Added by Keith B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Supreeta N

08/01/2023

Step 1

Notice that the exponentials \( e^{2x} \) and \( e^x \) suggest a substitution involving \( e^x \). Let \( u = e^x \). Then, \( du = e^x dx \) or \( dx = \frac{du}{u} \). Show more…

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Make a substitution to express the integrand as a rational function and then evaluate the integral. (Use C for the constant of integration.) ∫(3e^2x)/(e^2x + 15ex + 54) dx