Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Integrate by parts
- Integrate by partial fractions
- Integrate by substitution
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
- FOIL Method
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Applying the product rule for logarithms: $\log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right)$
Learn how to solve integrals involving logarithmic functions problems step by step online.
$\int\left(\ln\left(\sqrt[5]{x}\right)+\ln\left(\left(x^2-4\right)^7e^x\right)\right)dx$
Learn how to solve integrals involving logarithmic functions problems step by step online. Solve the integral of logarithmic functions int(ln(x^1/5(x^2-4)^7e^x))dx. Applying the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right). Expand the integral \int\left(\ln\left(\sqrt[5]{x}\right)+\ln\left(\left(x^2-4\right)^7e^x\right)\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int\ln\left(\sqrt[5]{x}\right)dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify u and calculate du.