Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Integrate by substitution
- Integrate by partial fractions
- Integrate by parts
- 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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We can solve the integral $\int r^2\left(\frac{r^3}{18}-3\right)^5dr$ 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 $\frac{r^3}{18}-3$ it's a good candidate for substitution. Let's define a variable $u$ and assign it to the choosen part
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$u=\frac{r^3}{18}-3$
Learn how to solve integral calculus problems step by step online. Find the integral int(r^2((r^3)/18-3)^5)dr. We can solve the integral \int r^2\left(\frac{r^3}{18}-3\right)^5dr 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 \frac{r^3}{18}-3 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 dr 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. Isolate dr in the previous equation. Substituting u and dr in the integral and simplify.