tentukan hasil pengintegralan berikut : a. integral (2x^2 + 3) dx b. integral (4x^8 + 2x^5 +3) dx c. integral 10 / x^4 dx d. integral 5x-4 / x^3 e. integral x^4

Integral

a. ∫ (2x² + 3) dx
= 2/(2+1) x²⁺¹ + 3/(0+1) x⁰⁺¹ +c
= 2/3 x³ + 3 x + c

b. ∫ 4x⁸ + 2x⁵ + 3) dx = 4/9 x⁹ + 2/6  x⁶ + 3x + c
= 4/9 x⁹ + 1/3 x⁶ + 3x + c

c. ∫ 10/x⁴ dx = ∫10 x⁻⁴ dx = 10/(-3) x⁻³ = -10/(3x³) + c

d. ∫ (5x-4)/x³ dx = ∫ (5x-4) x⁻³ dx = ∫ 5x⁻² - 4 x⁻³ dx
= 5/(-1) x⁻¹ - 4/(-2)x⁻²  +c
= -5/(x) + 2/x² + c

e. ∫ x⁴√ x dx = ∫ x⁴. x¹/² dx =  ∫ x⁹/² dx = 1/(11/2) x¹¹/² +c
= 2/11 x¹¹/²= 2/11  x²√x + c

f. ∫ 5x √x³ dx  = ∫5x .x³/²  dx = ∫ 5.x⁵/²  dx = 5/(5/2 +1) x⁵/²⁺¹ +c
= 10/7  x⁷/² +c  =  10/7 x³ √x + c
....