jwb :
∫ x√(5-x² ) dx
misal u = 5-x² → du = -2x dx → dx = (-1/2x)du
= ∫ -((xu^½)/2x) du
= -½ ∫ u^½ du
= -⅓u^(3/2) + c
= -⅓√(5-x²)³ + c
= -⅓(5-x²)√(5-x²) + c
2.Integral x^2 √(2-3x^3 ) dx ?
jwb :
∫ x²√(2-3x³) dx
Misal u = 2-3x³ → du = -9x² dx → dx = -(1/9x)du
= ∫ -((x²u^½)/9x) du
= -⅟₉ ∫ u^⅓ du
= -²/₂₇ u^(3/2) + c
= -²/₂₇ √(2-3x³)³ + c
= -²/₂₇ (2-3x³)√(2-3x³) + c
3. ∫ sin^4x + cos^4x + 2sin^2xcos^2x dx ?
jwb :
∫ (secx√(sec²x) – 1) dx
= ∫ sec²x dx - ∫ 1 dx
= tan x – x + c
