(1.) dx here is the problem

= -5x + C integrate

(2.) ∫ a dx here is the problem

= ax + C integrate

(3.) ∫ 10x dx here is the problem

= 5x² + C integrate

(4.) ∫(ax + b) dx here is the problem

= (1/2)ax² + bx + C integrate

(5.) ∫(1 + 2x + 3x² + 4x³)dx here is the problem

= x + x² + x³ + x⁴ + C integrate

(6.) ∫(1 - x + x² - x³ + x⁴)dx here is the problem

= x - (1/2)x² + (1/3)x³ - (1/4)x⁴ + (1/5)x⁵ + C integrate

(7.) ∫x^-5 dx here is the problem

= (-1/4)x^-4 + C integrate

(8.) ∫(12/x³)dx here is the problem

= ∫12x^-3 dx use a negative exponent

= -6x^-2 + C integrate

(9.) ∫7x^-1/2 dx here is the problem

= 14x^1/2 + C integrate

(10.) ∫[√x + (1/√x)]dx here is the problem

= ∫[x^1/2 + x^-1/2]dx use exponents for radical signs

= (2/3)x^3/2 + 2x^1/2 + C integrate