hasil dari integral x²√2x³-1 dx adalah?

Materi: Integral
Metode penyelesaian: Substitusi

Pembahasan di gambar

[tex]\displaystyle \text{misal :}\\2x^3-1=u\\6x^2\,dx=du\\\\\int x^2\sqrt{2x^3-1}\,dx=\int \sqrt{2x^3-1}x^2\,dx\\\int x^2\sqrt{2x^3-1}\,dx=\int \sqrt{u}\cdot\frac16\,du\\\int x^2\sqrt{2x^3-1}\,dx=\int\frac16u^\frac12\,du\\\int x^2\sqrt{2x^3-1}\,dx=\frac16\cdot\frac23u^\frac32+C\\\boxed{\boxed{\int x^2\sqrt{2x^3-1}\,dx=\frac19(2x^3-1)^\frac32+C}}[/tex]