Final answer to the problem
$\left(e^{4x}-1\right)\ln\left|e^{4x}-1\right|+\left(-e^{4x}-1\right)\ln\left|e^{4x}+1\right|+C_1$
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Step-by-step Solution
How should I solve this problem?
- Integrate by substitution
- Find the derivative using the definition
- Solve by quadratic formula (general formula)
- Simplify
- Find the integral
- Find the derivative
- Factor
- Factor by completing the square
- Find the roots
- Find break even points
- Load more...
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1
Find the integral
$\int\ln\left(\frac{e^{4x}-1}{e^{4x}+1}\right)dx$
Learn how to solve problems step by step online.
$\int\ln\left(\frac{e^{4x}-1}{e^{4x}+1}\right)dx$
Learn how to solve problems step by step online. Solve the logarithmic equation y=ln((e^(4x)-1)/(e^(4x)+1)). Find the integral. The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator. Expand the integral \int\left(\ln\left(e^{4x}-1\right)-\ln\left(e^{4x}+1\right)\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\ln\left(e^{4x}-1\right)dx results in: \left(e^{4x}-1\right)\ln\left(e^{4x}-1\right)-e^{4x}+1.
Final answer to the problem
$\left(e^{4x}-1\right)\ln\left|e^{4x}-1\right|+\left(-e^{4x}-1\right)\ln\left|e^{4x}+1\right|+C_1$
