Questions: ∫ (e^x - e^x) / (e^x + e^-x) dx

Transcript text: $\int \frac{\left(e^{x}-e^{x}\right)}{e^{x}+e^{-x}} d x$

Solution

Solution Steps

To solve the integral $\int \frac{\left(e^{x}-e^{x}\right)}{e^{x}+e^{-x}} d x$, we first observe that the numerator simplifies to zero because $e^x - e^x = 0$. Therefore, the integral simplifies to $\int 0 \, dx$.

Solution Approach

Simplify the integrand.
Recognize that the integral of zero is zero.

Step 1: Simplify the Integrand

Given the integral: \[ \int \frac{e^x - e^x}{e^x + e^{-x}} \, dx \] we observe that the numerator simplifies to zero: \[ e^x - e^x = 0 \] Thus, the integrand becomes: \[ \frac{0}{e^x + e^{-x}} = 0 \]

Step 2: Integrate the Simplified Expression

The integral of zero is: \[ \int 0 \, dx = 0 \]