Hasil dari ∫▒〖〖(4x〗^2- 〖4x)〗^2 〗 (2- 4x) dx=⋯

Hasil dari ∫▒〖〖(4x〗^2- 〖4x)〗^2 〗 (2- 4x) dx=⋯

Jawab:

$displaystyle text{misal:}\u=4x^2-4x\du=8x-4,dx\\int(4x^2-4x)^2(2-4x),dx=int(4x^2-4x)^2cdotleft(-frac12right)(8x-4),dx\int(4x^2-4x)^2(2-4x),dx=-frac12int u^2,du\int(4x^2-4x)^2(2-4x),dx=-frac12cdotfrac1{2+1}u^{2+1}+C\int(4x^2-4x)^2(2-4x),dx=-frac1{6}u^{3}+C\int(4x^2-4x)^2(2-4x),dx=-frac1{6}(4x^2-4x)^{3}+C$

Beberapa konsep yang dipakai:

$displaystyletriangleright~int(y_1pm y_2pmcdotspm y_n),dx=int y_1,dxpmint y_2,dxpmcdotspmint y_n,dx\triangleright~int ky,dx=kint y,dx\triangleright~int ax^n,dx=frac{a}{n+1}x^{n+1}+C~;~nneq-1$