Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Integrate by parts
- Solve by quadratic formula (general formula)
- Find the derivative using the definition
- Simplify
- Find the integral
- Find the derivative
- Factor
- Factor by completing the square
- Find the roots
- Exact Differential Equation
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Find the integral
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$\int\left(x^6+\frac{-6}{x^5}+e^{-4x}+\ln\left(3x\right)+\frac{-5}{x}\right)dx$
Learn how to solve problems step by step online. Simplify the expression f(x)=x^6+-6/(x^5)e^(-4x)ln(3x)-5/x. Find the integral. Expand the integral \int\left(x^6+\frac{-6}{x^5}+e^{-4x}+\ln\left(3x\right)+\frac{-5}{x}\right)dx into 5 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int\ln\left(3x\right)dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify or choose u and calculate it's derivative, du.