[tex] \displaystyle \int \tt \frac{ {z}^{2} \times {5z}^{3} - {4y}^{5} }{x \times {z}^{2} \times {y}^{3} \div {y}^{2} } \: dz[/tex]
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[tex] \tt \tiny{jawablah \: para \: suhu \: matematika}[/tex]
[tex]\begin{aligned}&\int\frac{z^2\times5z^3\:-\:4y^5}{x\times z^2\times{y}^3\div{y}^{2}}\,dz\\&{=\ }\ \boxed{\,\frac{5z^5+16y^5}{4xyz}\:+\:C\,}\end{aligned}[/tex]
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Integral
[tex]\begin{aligned}&\int\frac{z^2\times5z^3\:-\:4y^5}{x\times z^2\times{y}^3\div{y}^{2}}\,dz\\&{=\ }\int\frac{5z^5\:-\:4y^5}{xyz^2}\,dz\\&{=\ }\int\left(\frac{5}{xy}\cdot z^3\right)dz\:-\:\int\left(\frac{4y^4}{x}\cdot\frac{1}{z^2}\right)dz\\&{=\ }\frac{5}{xy}\int z^3\,dz\:-\:\frac{4y^4}{x}\int z^{-2}\,dz\\&{=\ }\frac{5}{xy}\cdot\frac{z^4}{4}\:-\:\frac{4y^4}{x}\cdot\frac{z^{-1}}{-1}\:+\:C\\&{=\ }\frac{5z^4}{4xy}\:+\:\frac{4y^4}{xz}\:+\:C\end{aligned}[/tex]
[tex]\begin{aligned}&{=\ }\frac{5z^4\cdot z+4y\cdot 4y^4}{4xyz}\:+\:C\\&{=\ }\,\boxed{\,\frac{5z^5+16y^5}{4xyz}\:+\:C\,}\end{aligned}[/tex]
[tex]\blacksquare[/tex]
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