tolong dong. materi integral kelas 12

Integral Substitusi

(7)
∫ [3 + ¹/₂.x]⁻⁸ dx
u = 3 + ¹/₂.x
du/dx = ¹/₂ ⇒ dx = 2 du
= ∫ u⁻⁸ (2 du)
= 2.-¹/₇.u⁻⁷ + c
= - ²/₇.(3 + ¹/₂.x)⁻⁷ + c

(8) 
[tex] \int\limits [{4x-7}^{ \frac{1}{3}}]dx [/tex]
u = 4x - 7
du/dx = 4 ⇒ dx = ¹/₄ du
[tex]=\int\limits [u^{ \frac{1}{3}}] (\frac{1}{4} du) [/tex]
[tex]= \frac{1}{4}. \frac{3}{4} [u^{ \frac{4}{3}}]+c [/tex]
[tex]= \frac{3}{16} (4x-7)^{ \frac{4}{3}}+c [/tex]
[tex]= \frac{3}{16} \sqrt[3]{(4x-7)^{4}} } +c [/tex]

(9)
∫ [3 - 2x]⁻¹ dx
u = 3 - 2x
du/dx = -2 ⇒ dx = - ¹/₂.du
= ∫ u⁻¹ (- ¹/₂.du)
= - ¹/₂.ln | u | + c
= - ¹/₂.ln |3 - 2x| + c

(10)
∫ x(x² - 3)⁹ dx
u = x² - 3
du/dx = 2x ⇒ dx = du/(2x)
= ∫ x.u⁹.du/(2x)
= ¹/₂.∫ u⁹ du
= ¹/₂.¹/₁₀.u¹⁰ + c
= ¹/₂₀.u¹⁰ + c
= ¹/₂₀.(x² - 3)¹⁰ + c