Question

Where did it go wrong in the following process? Integrate: $\int (e^x + e^{-x})^2 dx$ Step 1: $\int (e^x + e^{-x})^2 dx = \int (e^{2x} + e^{-2x}) dx$ Step 2: $= \frac{1}{2}e^{2x} - \frac{1}{2}e^{-2x} + C$ Step 1 Step 2

          Where did it go wrong in the following process?
Integrate: $\int (e^x + e^{-x})^2 dx$
Step 1: $\int (e^x + e^{-x})^2 dx = \int (e^{2x} + e^{-2x}) dx$
Step 2: $= \frac{1}{2}e^{2x} - \frac{1}{2}e^{-2x} + C$
Step 1
Step 2

Where did it go wrong in the following process?
Integrate: ∫ (e^x + e^-x)^2 dx
Step 1: ∫ (e^x + e^-x)^2 dx = ∫ (e^2x + e^-2x) dx
Step 2: = (1)/(2)e^2x - (1)/(2)e^-2x + C
Step 1
Step 2

Added by Lauren M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Mary Wakumoto

Step 1

However, the square of a sum is not equal to the sum of the squares. So, the expression should be expanded using the formula (a + b)^2 = a^2 + 2ab + b^2. Show more…

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Where did it go wrong in the following process? Integrate: âˆ«(e^x + e^-x)^2 dx Step 1: âˆ«(e^2x + e^-2x) dx Step 2: = âˆ«(e^2x) dx + âˆ«(e^-2x) dx + C