Final answer to the problem
$x-8\cdot \left(\frac{1}{\sqrt{12}}\right)\arctan\left(\frac{x+2}{\sqrt{12}}\right)-\frac{4}{3}\ln\left|\sqrt{\left(x+2\right)^2+12}\right|+\frac{4}{3}\ln\left|x-4\right|+C_1$
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Step-by-step Solution
How should I solve this problem?
- Find the integral
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Prove from LHS (left-hand side)
- Load more...
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1
Find the integral
$\int\frac{x^3}{x^3-64}dx$
Learn how to solve problems step by step online.
$\int\frac{x^3}{x^3-64}dx$
Learn how to solve problems step by step online. Find the integral of (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
$x-8\cdot \left(\frac{1}{\sqrt{12}}\right)\arctan\left(\frac{x+2}{\sqrt{12}}\right)-\frac{4}{3}\ln\left|\sqrt{\left(x+2\right)^2+12}\right|+\frac{4}{3}\ln\left|x-4\right|+C_1$
