Final Answer
$\frac{512}{9}z^{9}+\frac{384}{7}z^{7}+\frac{96}{5}z^{5}+\frac{8}{3}z^{3}+C_0$
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Step-by-step Solution
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1
Rewrite the integrand $z^2\left(8z^2+2\right)^3$ in expanded form
$\int\left(512z^{8}+384z^{6}+96z^{4}+8z^2\right)dz$
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$\int\left(512z^{8}+384z^{6}+96z^{4}+8z^2\right)dz$
Learn how to solve problems step by step online. Find the integral int(z^2(8z^2+2)^3)dz. Rewrite the integrand z^2\left(8z^2+2\right)^3 in expanded form. Expand the integral \int\left(512z^{8}+384z^{6}+96z^{4}+8z^2\right)dz into 4 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int512z^{8}dz results in: \frac{512}{9}z^{9}. The integral \int384z^{6}dz results in: \frac{384}{7}z^{7}.
Final Answer
$\frac{512}{9}z^{9}+\frac{384}{7}z^{7}+\frac{96}{5}z^{5}+\frac{8}{3}z^{3}+C_0$