Review sheet answers

Integrals (problem 1)

Substitute x = (u^3)

∫(1/(x (1  +  (x^(1/3))))) \[DifferentialD]x

See textbook example, page

∫Tan[x]^3 \[DifferentialD]x

In tegration by parts.

∫x (E^(-2 x)) \[DifferentialD]x

In tegration by parts.

∫(x^2) Log[x] \[DifferentialD]x

Rewrite the integrand as follows:

Sin[x]^3 Cos[x]^4
% /. Sin[x]^3 -> (1 - Cos[x]^2) Sin[
            x]
Expand[%]

Trig substitution or integration by parts.

∫((x^3)/(Sqrt[4 + (x^2)])) \[DifferentialD]x

Trig substitution or integration by parts.

∫((x^3)/(((4 + (x^2)))^(3/2))) \[DifferentialD]x

Partial fractions expansion.

∫(((x^2) + 
                2 x)/(((x^2) + 
                    4) (((x - 1))^2))) \[DifferentialD]x // 
      Expand