Question

Problem 5. Compute the following (a) $\int \frac{e^{2x}}{\sqrt{e^{2x}+3}} dx$ (b) $\int \frac{e^{4x}+e^{x}}{e^{2x}} dx$ (c) $\int_{1}^{3} t^{-4/5} e^{t^{1/5}} dt$

Name: problem 5 compute the following a int frace2xsqrte2x3 dx b int frace4xexe2x dx c int13 t 45 et15 dt 89124
Uploaded: 2022-03-02T21:01:56-08:00
Duration: 1 min 45 s
Channel: Gregory Higby
Description: problem 5 compute the following a int frace2xsqrte2x3 dx b int frace4xexe2x dx c int13 t 45 et15 dt 89124

          Problem 5. Compute the following
(a) $\int \frac{e^{2x}}{\sqrt{e^{2x}+3}} dx$
(b) $\int \frac{e^{4x}+e^{x}}{e^{2x}} dx$
(c) $\int_{1}^{3} t^{-4/5} e^{t^{1/5}} dt$

$problem 5 compute the following a int frace2xsqrte2x3 dx b int frace4xexe2x dx c int13 t 45 et15 dt 89124$

Added by Charles W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Gregory Higby

03/02/2022

Step 1

Then $du = 2e^{2x} dx$, so $e^{2x} dx = \frac{1}{2} du$. The integral becomes $\int \frac{e^{2x}}{\sqrt{e^{2x}+3}} dx = \int \frac{1}{\sqrt{u}} \frac{1}{2} du = \frac{1}{2} \int u^{-1/2} du = \frac{1}{2} \frac{u^{1/2}}{1/2} + C = u^{1/2} + C = \sqrt{e^{2x}+3} + Show more…

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Problem 5. Compute the following (a) $\int \frac{e^{2x}}{\sqrt{e^{2x}+3}} dx$ (b) $\int \frac{e^{4x}+e^{x}}{e^{2x}} dx$ (c) $\int_{1}^{3} t^{-4/5} e^{t^{1/5}} dt$