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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Rewrite the expression $z^2\left(8z^2+2\right)^3$ inside the integral in factored form
Learn how to solve integral calculus problems step by step online.
$\int8z^2\left(4z^2+1\right)^3dz$
Learn how to solve integral calculus problems step by step online. Find the integral int(z^2(8z^2+2)^3)dz. Rewrite the expression z^2\left(8z^2+2\right)^3 inside the integral in factored form. The cube of a binomial (sum) is equal to the cube of the first term, plus three times the square of the first by the second, plus three times the first by the square of the second, plus the cube of the second term. In other words: (a+b)^3=a^3+3a^2b+3ab^2+b^3 = (4z^2)^3+3(4z^2)^2(1)+3(4z^2)(1)^2+(1)^3 =. Solve the product 8z^2\left(\left(4z^2\right)^3+3\left(4z^2\right)^2+12z^2+1\right). Solve the product 8\left(3\left(4z^2\right)^2+12z^2+1\right).