Question

Evaluate:∫(ax+b)^3dx

Answer 1

solution

∫(ax+b)∧3 dx

using integral by substitution

let u=ax+b ⇒du/dx=a ⇒dx=du/a

then we substitute

∫u∧3*du/a

1/a∫u∧3du

1/a((u∧4)/4) + c

=(u∧4)/4a + c

⇒=(ax+b)∧4/4a + c