how to solve integration of (3x+5)^4

Question

how to solve integration of (3x+5)^4

Answer 1

Let f(x) = 3x + 5

 

∫(3x + 5)⁴dx = (1/3)∫(3x + 5)⁴(3dx)

 

Now you have an integral of the form 

 

∫f(x)ⁿdf = f(x)ⁿ⁺¹/(n + 1) + c

 

∫(3x + 5)⁴dx = (1/3)∫(3x + 5)⁴(3dx) = (1/3)(3x + 5)⁵/5 + c = (3x + 5)⁵/15 + c

 

You could also do a binomial expansion of the integrand and integrate the resulting polynomial term by term, but that would be tedious.