Question

Evaluate the following integrals
(i) ∫(𝟑𝒙 + 𝟕)
𝟒 𝒅𝒙
(ii) ∫ 𝟒(𝟐𝒙 − 𝟑)
−𝟐𝒅𝒙
(iii) ∫√𝟓𝒙 + 𝟏 𝒅𝒙

Answer 1

for (i) and (ii) would you mind clarifying/re-typing the integrals?

as for (iii), remember the reverse of the derivative rules for exponents and constants

\[\int\limits_{}^{}x^{n} dx=\frac{ x^{n+1} }{ x^{n} }+C\]
in your case, the first part of the integral is sqrt(5)x^1. integrate x^1 using the above rule, then simply stick the coefficient of sqrt(5) in front of the integral

the next part of the integral (the +1 part) is a constant, so the integral is just 1*x for that part