Final answer to the problem
$x-8\cdot \left(\frac{1}{\sqrt{12}}\right)\arctan\left(\frac{x+2}{\sqrt{12}}\right)-\frac{4}{3}\ln\left|\sqrt{\left(x+2\right)^2+12}\right|+\frac{4}{3}\ln\left|x-4\right|+C_1$
Got another answer? Verify it here!
Step-by-step Solution
How should I solve this problem?
- Integrate using basic integrals
- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Product of Binomials with Common Term
- FOIL Method
- Load more...
Can't find a method? Tell us so we can add it.
1
Find the integral
$\int\frac{x^3}{x^3-64}dx$
Learn how to solve one-variable linear equations problems step by step online.
$\int\frac{x^3}{x^3-64}dx$
Learn how to solve one-variable linear equations problems step by step online. Integrate the function (x^3)/(x^3-64). Find the integral. Divide x^3 by x^3-64. Resulting polynomial. Expand the integral \int\left(1+\frac{64}{x^3-64}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately.
Final answer to the problem
$x-8\cdot \left(\frac{1}{\sqrt{12}}\right)\arctan\left(\frac{x+2}{\sqrt{12}}\right)-\frac{4}{3}\ln\left|\sqrt{\left(x+2\right)^2+12}\right|+\frac{4}{3}\ln\left|x-4\right|+C_1$
