Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Integrate by substitution
- 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
- Load more...
Find the integral
Learn how to solve problems step by step online.
$\int\left(x^6+\frac{-6}{x^5}+e^{-4x}+\ln\left(3x\right)+\frac{-5}{x}\right)dx$
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 e^{-4x}dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that -4x it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above.